Maxima won't start
 

We have a 96 Maxima and it will not start. Turn the key and the starter kicks in and engages the flywheel then kicks right back out. Will do this all day long. Pulled the starter off and took it to two different places to have it tested and the starter was good but the solenoid was bad. Bought a new solenoid, put it back together and it does the same thing. I can use a screwdriver and arch the solenoid and it does the exact same thing. Any thought?