hard starting problem

I'm having an issue with my '89 camry v-6. My daughter drives it varying distances and when she turns the engine off, the car won't start until it cools down. (ususally 20+ minutes) I replaced the starter twice just in case I had a bad rebuild. The battery was checked and found to be good. I finally gave up and took it to a real mechanic and they replaced the starter once again stating that the AC-Delco was problematic. It now has a Nippon-Denso installed(to the tune of $300) I'm still having the same symptoms and now the mechanic wants to install a new ingnition switch.
1. Could that indeed be the problem?
2. How hard would it be to replace that myself?
3. What kind of cost should I be looking at for parts and labor?
As always, I appreciate your help and comments--Keith

Won't start means it won't crank, or cranks and won't fire?

Assuming it won't crank, did you check the starter relay?

Won't start means it won't crank, or cranks and won't fire?

Assuming it won't crank, did you check the starter relay?
It will not crank at all. We have found, however, that by turning the key slowly our problem is diminished. The starter relay is located where?

Thanx Brian, I will check that relay post haste--K

You're welcome. I hope that is your problem.