2002 Dodge Caravan Check Timing Will Enging Run Belt Off 1 Tooth Changed Year

If the engine runs normally for a week, you know the timing belt is okay.

It sounds like you're confusing a locked up engine with an intermittent starter problem. A locked engine is very serious and isn't going to fix itself by turning the ignition switch. What you're describing is a common problem caused by worn contacts in the starter solenoid. There are repair kits that cost around fifteen bucks, but most people just replace the entire starter.