What else could be causing this problem? Next step?

Car would not crank, took the key out of the ignition and it tried to crank itself so I put the key back in the ignition and it cranked that time but made a squealing, grinding noise when in park. I drove down the road put it in park it did it again but when put in park a third time it was fine. I drove home and a few hours later it would not even turn over. I replaced the battery and the starter and solenoid but it still won't crank. All lights, radio, etc are working fine but it won't even turn over.