1997 Cavalier

I just bought a used 1997 Cavalier. It needed a battery. Jumped it to get it home. Found the battery was toast, they charged it at Advanced and it stunk up the place and after being charged to 12v, within 1 hour, not in the car it dropped to 4v. Bought a new battery and a new starter solenoid assembly. I also cleaned the engine and engine areas to degrease.

Now it will not start. When someone turns the key to start, I do not get 12v to the starter solenoid. The starter side has its 12v because it appears to be hardwired.

All the dash lights come on as usual.
The antitheft light is solid not blinking.
The lights and radio clock all dim when moved to start position as if it is trying to start.

Found one thread that mentioned the crankshaft position sensor. Can I test this?
Any other suggestions?

Towing it to the shop not a financial option this month.