97 Corolla (sometimes) won't start

Toyota starter solenoid contacts frequently wear out (6-10 years is typical). If you’re handy, you can remove the starter, take off the solenoid, and replace the contacts for less than $30. Here’s a description of what’s involved (make sure you get both the side contacts and the center disk).
Here’s how: http://www.yotarepair.com/startercontacts.html