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

Park/Neutral safety switch.

The P/N safety switch is part of a combination switch mounted to the transaxle. This switch determines whether the transmission is in park or neutral in order for the starter to operate, It turns on the back-up lights when the transmission is shifted into reverse, and it tells the computer what gear the transmission is in.

This switch is made of plastic and heat can effect the switch.

Tester