2004 Nissan Quest - Shuts off

car shut off after 15 minutes after driving

Are you saying the van keeps running for 15 minutes after you shut off the ignition or that it dies after it’s been running for 15 minutes?

The problem might be a crankshaft position sensor being effected by heat.

If you wait long enough, the sensor cools down, the engine restarts and runs until the sensor gets hot again, and the engine shuts off.

Tester

I assume you can’t get it started now after that happened. One possibility if that is the case is a timing belt has broken. If that is the case then there may be some valve damage if the engine is the interfering type. Checking the compression will tell the story about that. Check the codes for possible clues to the problem.