2000 Taurus doesn't turn over
 

My nephews car decided not to start for him. When you turn the key dash lights come on but nothing else happens, no clicking or anything. The battery is charged. I used a screw driver to jump the starter , I could hear it spin but It did not engage the fly wheel. Shouldn't it engage the fly wheel if I jump it like this? I took the starter off and took it to auto zone and had it tested and it passed all tests but the guy at autozone showed me that the start post on the solenoid was really loose. Could it still be the starter or should I start looking else where for the issue?