Corolla won't start

Hi. I've got a '99 Toyota Corolla CE, auto transmission. My wife had a problem starting the car. When I tried it, I tried jiggling the 'Park' gear position of the shifter and nothing happened - I couldn't even push in the nob to shift to a different gear. No lights, no windshield wipers, nothing worked. So I got out to push the car - just a few inches and that seemed to unlock it. Now the lights worked, I could shift gears and magically the car started! So, what's wrong? The same thing happened to us about 2 weeks ago (only at that time I hadn't tried to push the car). The mechanics couldn't replicate the problem (it started for them every time!), but they replaced the starter at a cost of $400! Any help would be appreciated. I certainly don't want to have to pay for another starter after just 2 weeks!
Thanks,
Mark B.

Gremlins
:)