Iwould suggest bench testing the old starter (hook it up to your jumper cables and jump the solenoid)
It should kick hard and spin enthusiasticly.
If it does work, you problem is for sure in the car's wiring.
if it just 'click', or whines and turns @2RPM like the last one I changed, you may have got a defective replacement unit. It happens enough that I usualy test them before installation, esp on cars that take more than 5 minutes for a starter swap.