Most places that sell batteries should be able to test yours (a straight across the terminals voltage test is not enough)... you need to know how the voltage drops under load.  The outcome of such a test will allow you to tick the easiest (to fix) problem off your list.

Current is directly related to starter torque.  You obviously have enough current flow to spin the motor with no compression. So the next step is to carefully check the complete battery to starter and starter to earth current path (either remove and clean or just measure (hopefully 'lack of') resistance across the terminals).  

Finally you can check the starter -  although someone more technical than I will have to advise how ..Doug L??  I just take mine to a mate.

A new motor will be stiff but that, +10:1 compression, should not be too much for a starter in reasonable health.....

Once you get it cranking then you can look at the other issues... if indeed there are any.

In the meantime, perhaps gather a few mates and try a push start??

Cheers, Ian

I had a similar experience with my new, high compression rebuild. Normal turn-over with the plugs out—very slow w/ the plugs in. I replaced the battery and swapped out my new, stock starter for a high-torque model. That helped, but as the motor acquired more miles things settled down to normal. Not saying that you may or may not have other issues, but new motors can be tight.

Don't assume anything if you did not do the work yourself.  

It acts the same whether you push the clutch or do not.  I tried the jump start method and it maybe spun the engine a wee bit better but still about what you'd expect if the battery were pretty dead.  I tried just pulling one plug out and it spun about as well as it did with the jumper method.  

On the engine rebuild, I inherited the engine and the car project.  The engine was rebuilt by a reputable firm with a lot of experience so I have to assume they knew what they were doing. 

For now the battery is on the trickle charger to power it back up and I'll try some experiments tomorrow.

Are you pushing in the clutch pedal when attempting to start with plugs in and not when cranking with plugs out?

If so may point to a clutch and/or thrust bearing issue.

Bad connections can be points of high resistance which restrict current flow.  So yes, you should clean all the connection points.  However, before the engine rebuild how did the engine turn over?

I have a few questions which echo what you have already been asked or received as suggestions.

• When you put the timing pulleys back on did you set the VALVE timing dot-to-dot or did you use a degree wheel?
• When you put the head back on did you adjust all the valves?
• Did you install the distributor drive gear in the block to match the positional information shown in the service manuals?
• When you put the distributor back in the block did you set the static IGNITION timing AND did you make sure you were setting the timing with #1 (water pump end of engine) near TDC on its FIRING stroke?

Charged the battery overnight and it still just barely turns it over.  The wiring all seems fine when I checked it this morning.  If you pull the spark plugs the starter spins the engine over like a top.  If it were a bad connection wouldn't that affect turning the engine over with the plugs out too?  

+1 for weak battery. Put a fresh charge on it overnight and give it another whirl. If necessary, put a second battery on it using jumper cables straight onto the starter solenoid up front vs onto the original battery terminals.

Timing, fuel etc won't matter a hill of beans if the starter won't (or hardly) turn the motor over....

Earth checks first, power connection second and then perhaps try to borrow another starter.  If that's not an option perhaps a local auto electrician might be able to test the starter???

I've just had similar issues until the local battery shop pointed out that they sold me the current battery around 12 years ago.  New battery and it starts first flick of the key.  You said you have a new battery but the connections may still be suss.

Cheers, Ian

It would cough if fuel was there. You didn't mention if you had mechanical or electric fuel pump or if you had fuel in the carb. I'm with willie & Vespa's comments. I would check the following:
1) proper ground 
2) timing
3) starter

Wouldn't the engine turn over but not fire if things were connected wrong?  Wouldn't you get some sort of coughing, backfiring, etc.?  There is no noise other than the noise of it turning over once.  You can watch the fan and it only makes one revolution then it stops and then it makes another half revolution, then it's nothing.  

are you 100% the timing is correct and not 180 degree's off
i would start with making sure the timing is correct and you have the 
spark plug wires correct,  

Make sure your engine ground is good?clean on both ends. Could be an old/weak starter like you mentioned.

I've gotten to the point in the rebuild where I am trying to start the new engine.  I put in new oil, pulled the plugs, and then cranked it a bit to circulate the oil.  The engine spun over just fine, the fan and alternator were spinning nice and fast.  So I put the plugs back in and tried to start it.  All it will do is slowly turn over once, then pause, then turn over real slowly about a half turn, then nothing.  What would be a possible issue?  Could the old starter not have enough umph to turn over the new engine?  The new one is a higher compression (10:1) than the old one.  It is a brand new battery.