Will not crank

I do not have a repair manual or wiring diagram for an Eunos but if this has a starter relay listen or put your finger tips on it and feel if it clicks one time when the key is turned to start. If it does, check any fuse that is for the starter. If the relay does not click, make sure the voltage from the ignition switch is making it through any neutral safety switch or clutch switch to the starter relay and this may also have a fuse as well.

The car when you turn the key tries to crank and the belt turns, but it seems that not enough power is going to it in order to make it start fully. I have tried to jump start it from a working car and it does the same as the battery installed.

Do either of the battery cables get really hot or smoke while trying to start?
If so, the cable that gets hot or smokes may be bad.
If you have a voltmeter place it on the battery, make sure you have 12 volts with the key off, then when the key is turned to start, the battery voltage does not drop below 9.6 volts when the starter is cranking.
Also, check the ground, take that jumper cable black cable place one end on the engine block and the other end of that black jumper cable on the negative battery post to make sure you have a good ground and try the starter again.

Cables do not get hot. Voltmeter shows 12.5 volts. Drops to 11 volts when trying to start.

Did you check the ground?

Done that. Still hardly anything.

Did the engine recently overheat or anything else go wrong with it that might cause it to partially seize?
Can you turn the engine over by hand?
Is this starter new?
Remove the spark plugs to relieve all the compression, disable the ignition so it does not spark, maybe by removing the ignition fuse or relay and then try the starter again with no compression, it should be easy now.

Starter motor is new. Battery is new. Car was laid up over winter for four months. I took out the spark plugs and engine does crank easily then. If I bump start the car (push start using clutch) the car runs fine. Never had a heating problem. Car has run today with bump start. Just cannot get the starter motor to crank when plugs are in.

Can you post an audio recording of how the starter sounds when cranking over with spark plugs in?

Here is the requested video.

You mean to tell me the belt is moving when you do that, because that does not sound to me as though the starter is cranking over at all.
Can you post another one except this time since it is a video, show if the belt is moving or not along with that noise.

Here is the next requested video. Thanks for the help by the way.

Check how much voltage is present at the starter when doing that, where the big positive battery cable is located on the starter.