I was able to start it by jumping the solenoid but the next time ... He initially thought it might be the push button start but when he tried it, he did not think that was the problem.

The soffits may have been cut too short, so push the screen mold in far enough ... If the squeaks persist, remove the hinge ...

If you need a circuit that converts a momentary push button to a latching switch with low standby current, this design might ...