starting problems

Would be handy to know how many amps the starter is drawing and what the voltage is dropping down to during cranking.

Manual or automatic? Is it possible that the clutch is not fully releasing and creating additional load on the starter?

What happens when the solenoid is jumpered at the starter? If it still labors then it is unlikely to be external to the starter solenoid circuit.

How hard is it to turn the motor over by hand?

Why did the original starter go out?

Are you positive that ALL of the connections are clean and tight? This includes the positive and negative sides of the battery? Is the braided ground strap from the left hand motor mount to the frame rail connected, clean, and tight?

Excellent advice above.

I would go back over those new connections/terminals. Sounds like one is resistive. Not that I condone testing it due to the possibility of injury, but if a connection gets real hot after trying to start the car, you've found a resistive bottleneck.

Is the starter turning over the engine normal fast....but not firing up.
Or is the starter turning the engine slow and slugish and firing late?

ground strap +1