05' Vibe Starts and runs fine, turn off the car, then it wont start back up

I don’t think this car is a lemon. 8 years and 170,000 miles is not an uncommon lifespan for the contact points on Toyota starter motor assemblies. What happens is that when you start the car, a mechanism in the starter assembly closes four contacts in the starter assembly to complete the starter motor ciruit. They tend to get fried (material erosion and carbon deposition) after a time and become intermittant. Typically when this happens you’ll occasionally hear a “click” but the start motor won’t turn the engine over.

Tester may be right. Your description fits his suggestion. I’m only offering another possibility to consider.