1999 Toyota Camry, approx 200,000 mi, 4-cyl

I have had intermittent problems with starting my car in hot temperatures (over 100 deg F); it only clicks. Usually, I could get it to start after a little time and additional attempts, but it would idle rough for about a minute then even out.

The last time this occurred, my car made a funny squeaking sound (not quite like a belt squeak). When I turned the ignition off and had the key in my hand, I discovered that the squeak was my starter still trying to turn over the engine. I replaced the key and only had to turn it to the on position for the car engine to turn over. This continued until I finally got the battery disconnected. The starter was smoking badly and shows signs of having been burned out (so, I think it's safe to say it needs to be replaced). Even now, if I hook up the battery the starter attempts to turn over briefly, but there is no electricity going to the rest of the car (so, I can't close the sun roof or windows). Is this a problem with the ignition switch? What else could be contributing?

I'm a college student and will be trying to repair the vehicle myself because of cost.

Thank you for your help.