DING DING DING!!!!!  The fob battery is the VERY last thing I would have thought of. Thank you AZmo! you saved me who knows how much time and how many forehead scars! Thank you, Thank you! I took one apart and checked. It was .62v in a 3v battery. Swapped it out for a new one and whirr, click, vroom. Can't thank you enough!!!!!

I have two MPI's and on both of them when you "disarm" the alarm/immobilizer the light on the dash should go off. The only time it's on solid is when the doors are open (a strain on the battery).
You should hear a slight hum when the key is turned for a couple of seconds, that would be the fuel pump priming the injectors.
Have you tried to change the batteries in the fobs?  

If you have power to the starter solenoid just jump the solenoid if it still does not start tap the solenoid with the handle of a screwdriver sometimes they freeze up when sitting.
You also may need to re set the key fobs.

Thank you very much! That's good info. I think it's an entirely primary starting circuit issue but I haven't had the time yet to backtrack it. Thanks!

Drufly says that fuel pump works by clicking. I've only experienced a whirling sound at the turn of the key. I'm not sure if the MPI has fusible links, but I would think they would be a carry over.

I doubt there are any problems with the immobilizer - if it wasn't working, there should be no energizing of the fuel system at all (no clicks or anything.) As far as I know, the immobilizer doesn't affect the starter circuit separately - if the fuel system is activated, then everything else is too.

Go back to basics - is there spark? Pull a plug and see if there's sparking. If the plugs are wet, then you know you have fuel but no spark. If they're dry and you have spark, then back to the fuel system.

Is there voltage at the starter when you try to crank? If low, it may be the battery is worn out (despite the maintainer) and cannot power the starter, or even the relay enough to make it click. If no voltage, then there's where your problem is.

One of the most common fuel problems on these injected Minis is the fuel relay box above/behind the brake servo, but if it fails, then there would be no fuel pump power. (they usually signal their impending demise by not shutting the car off after you turn off the key - car keeps running.)

To keep the car original...

Why are you still using the alarm/immobilizer? It's over twenty years old. You're just asking for trouble.

I put my Rover Mpi away last fall. Everything was fine. I had a battery tender on it. I started it a couple of times over the winter. Everything was fine.

Today I tried to start it. Pushing the button on the alarm fob changed the state of the alarm light on the dash...went from blinking to solid just like normal. Turned the key...nothing. Headlights are bright, fuel pump clicks, horn works, etc but no noise out of the starter or solenoid at all. I pushed the crash immobilizer button but that was already set and had no effect. Tried the other fob and that didn't help either.

This weekend I'll look deeper for the obvious, fuses, loose connections, corrosion, mouse chew, etc. Hopefully it'll be an easy fix whatever it is.

Any members with Mpi experience who can point me in any other directions that aren't so obvious?

Thanks!