The MEMS systems are pre-OBD and somewhat unique, making it difficult to diagnose things without a proper reader.
Grounds are really important.

//www.tmsmini.com/cooper/pdf/MPi%20grounds.pdf

The ecu does not go bad that often hopefully you are lucky.

Ah, didn't realize the "MEMS" was the ecu itself. 

This makes it all the more worrisome. Hopefully he can sort the unit out himself. If any fun information comes out of him, I'll update. Looks like an expensive problem though 

The grounds and the MEMS ecu are all under the hood/bonnet. it is common for them to get corroded over the years especially if it is a UK Mini.
He may have by passed the fuel shut off switch also under the hood to the right of the air filter box.

Gave up / realized I was in over my head.

It's been 2 years since I REALLY drove the thing more than a couple dozen kms. So I took it to an auto electrician. 

He's getting back to me today. But so far he's been able to bypass (something) and get it starting reliably. He states he believes there is a bad ground in the "MEM UNIT/MODULE" 

I've given him all my haynes / electrical manuals so I have no idea where that unit is. Hopefully he's able to figure it out. 

Trim off the frizzy fibres, cut back the wire sheath about 2 to 3 inches, clean the insulation on all the wires and make a note of their colours.

Report what you find.

Also, remove your starter and inspect the bendix gear drive is OK. Put it in a vise or secure it to something solid. Connect it to a good battery. Using a screwdriver, short briefly from the battery terminal to the terminal corresponding to the one in my first picture that has the red stripe. A brief touch will make the solenoid kick and possibly spin the bendix gear.

You could remove the battery, give it a long (24 hours), low amperage charge, then have it load tested to be sure the battery is ok. If it is, reinstall with cleaned connections at both ends of the battery cables (4 locations), and then see where you are at.

I'm about 45-60min west of Toronto. between hamilton/toronto

Crappy Picture of my starter pre-disassembly

I attached a pic here that I took before I took all the wires off, the nut on the left side. I can clearly see 1 Large from the battery(on top), and two smaller (under that large wire)

While reattaching there is a 4th wire. about the size of that larger wire, which I'm unsure it's location. If memory serves me correctly its coming from that back of 4x30amp fuses. it looks almost identical to this larger wire here, except it's got a corrugated protective sheathing over it. The connector LOOKS like it want to connect on this starter solenoid, and reaches that location just fine. 

However if memory serves me correctly (which obviously at this point is suspect in general) When I USED to start the car, even with a low battery, or a dying battery. I never witnessed the voltage meter in the car (gauge on the dash) dip like this. If it was toast it would just hover around 8-10 and dip a little if you tried to start. This shows a strong 12ish and when you try to crank VIOLENTLY drops to zero immediate as the starter tries to engage. Part of me wants to try jumping it off my other car to see if it's the battery. But if i've cross wired something I don't want to do any more damage than I already potentially have. 

Graham: where are you located in Canada?

A dead battery will show 12V+/- on a voltmeter when there is no load on it. Add a load and the voltage drops drastically. A dead battery also might have enough juice to trigger the solenoid - the "click" - but not crank the engine. A dead battery may also be able to toot the horn or run some light loads such as instrument lights.

A test: watch your volt meter as you turn on various lights etc. Parking lights might show a dip, Add headlights and it would dip some more. Flash high beams and more dip. Turn on the heater fan and you should see a significant drop. Rear window heater the same thing.

Batteries can die suddenly when a cell salts up. One trip might be fine but the next start doesn't happen.

As for your stater wiring, you need to describe the colours of each wire you have - both its main colour and its trace line colour. If you have a ballasted ignition coil, you will have an additional wire than if you have a regular coil.

A rough guess from my Haynes book is that your starter should have a very large cable (from the battery) going onto a large terminal post and a white wire with red trace going to a smaller terminal. The white+red comes from a relay on the relay module. it is the trigger wire that activates the starter solenoid when you turn the key. The diagram doesn't show anything else connected directly to the starter. it shows a terminal between the battery and the starter that has 4 wires coming off it, which may be all brown. One feeds 4 fuses (always powered). One feeds the ignition switch which in turn feeds a light green+white trace going to 4 fuses powered when the ignition is "on". One supplies power (unfused) to several relays. The last one would be the charging wire coming from the alternator. All these four smaller wires may be on spade terminals on a terminal post or on the main battery post at the starter.

What year is your MPi?

Attached are photos of the starter on my carburetted 1981 Mini. Your wires may vary.
The white+red looks brownish, but you can see the red trace.
The white+yellow is the extra wire you may not have - it supplies 12V to the coil only during starting.

Does anyone by chance have a photo of the solenoid/starter installed?

I had the same issue the wire between the solenoid and starter had rotted out. Got a guy locally to fix the wire on the starter. But didn't take enough pictures of the starter before I ripped it out. 

I thought I wired it back up correctly (MPI mini), however now when I go to start it the volt meter in the car instead of dipping slightly drops right to zero. And the starter makes a loud CLICK (not like clicking the relays/solenoid makes when low on power) it sounds like the starter ger sliding out into place, but not actually spinning. 

I had the started tested when it was out after the guy fixed it. it worked well. I'm just at a loss of where to go from here. Can't seem to understand the wiring diagram. and I think I might have ****ed up the wiring. 

Ignition switch wire is on the same pin it was on before, that I know for sure.

I've got 2 thick wires, one is power from battery, the other is from the 30amp fuse panel. Both of these are on the +'ve solenoid terminal. as well as two thinner wires on that +'ve terminal. 

Then there is the new fixed wire the guy wired from the other terminal on the solenoid down into the starter motor itself. 

I feel like I'm missing something here. The only thing my pictures don't quite show is if BOTH of those thicker wires should be on the +'ve of the solenoid. the one from the battery, and the one from the 30amp fuse box.

I'm at a loss as to why the 'voltage meter' on the car dashboard no longer stays up near 12v. It used to dip slightly when trying to start (like maybe down to 10-11v) and now it just fully drops to 0v and the starter sounds like its "CLUNKING" into position but not trying to start the car or spin in any way

very frustrating. 

that was easy.

It turns out that the problem was the wite that connects the starter motor to the solenoid was broken. Thank you all for your help!! 

Since you are not getting the starter to engage I would start with the white / red wire at the ignition. Take a sewing needle or straight pin and stab it through up near the multifunction black box. Put a multimeter and see if it is live as you turn the key.

Also you need to check the brown color wires by the air cleaner the same way.

Again, I know nothing about MPI cars so the information below is generic.  Others more familiar with MPIs will need to correct my advice.

In the following test you are bypassing the starter relay. 

Locate the starter solenoid which should be piggy-backed to the starter motor.  On the solenoid there should be a threaded stud with a whole bunch of brown wires.  Near that should be a male spade lug with a brown/red wire on it.  Remove the brown/red wire from the solenoid and replace it with a short 16 gauge jumper wire.  Place the car in neutral.  TAP the other end of the jumper wire to the threaded solenoid terminal with all the brown wires on it.  There will be some small sparks.  Hopefully the starter will spin up when you touch the jumper wire to the the threaded solenoid terminal.  If the starter motor spins, that indicates the starter and its solenoid is OK.  If the starter doesn't spin, that indicates a solenoid or starter motor problem.  This test won't necessarily tell you what is wrong, just which direction to go next with troubleshooting.

Smack the starter solenoid a few times and give it a try. (with something hard like a hammer) .. (its little smaller canister on top of the actual starter)

 Solenoid Sounds stuck.. Wont solenoid engage to engage starter.

 Jump a screwdriver across the two large terminals of the starter solenoid and see if the starter engages motor... Likely to define the bad starter solenoid

Ensure your battery is good ( but if it wont starter motor with a jump = likely culprit is the starter)

The starter motor doesn’t crank the engine at all. The only way I can get it to run is with a bump start. Even jump leads won’t work 

Yeah that’s what I mean. It won’t start with jump leads, only a bump start 

That was my point Dan.  If by "bump start" the OP means he can push or roll start the car then the ignition system is more-or-less OK and attention has to be turned to whether or not the starter motor can be made to spin.  If he meant "jump start" (with cables)... and the engine will run (as stated in the OP's second post) when jumped, then the ignition AND starter work and attention would turn to a possibly weak battery. 

The key question for me is what does the OP mean in his second post when he says... " it’s weird as it will run with a bump start "  (Engine run or starter turn over?  Push or jump?)

You say it will start with a bump start (assuming Doug Lawson's definition is correct). Does the starter motor crank the engine at a decent speed? Have you tried a jump start using another known-good battery? Batteries these days often die a sudden death, often as you describe - between trips. They may read 12V on a meter and be able to power lights and other accessories, but don't have the oomph to provide cranking power and system voltage to run things like injection systems. Check also the battery cable connections are clean and tight.