I've never played with it, some switches do have 'play' in their contacts. MOST DON"T, so you may be onto something, if the thing has come apart inside, it will have 'play' and probably no contact - which would indicate the top is not open and ready to move, so the motor won't be commanded to start.

The "top open" switch (the one on the passenger side, in the top itself) is bypassed by taking the wires off the switch and connecting them together. It will tell the computer the top is always open, so it SHOULD go up and down if the switch was the problem.