Why did my car not move for several minutes in drive

Hello, if you are certain the shift lever did not inadvertently move out of the drive gear selection, then you could indeed have some kind of internal transmission issue occurring. Hands on testing would be needed using a diagnostic tool suitable for Toyota products and duplicating the concern while testing it. It's not a common concern, for sure, but anything is possible. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops