The fob is black, pear shaped about two inches long and just over an inch at the widest part, it locks and unlocks the
doors and has the red 'panic' button., the ignition key has a black plastic with the Rams head. The unlock rubber button
came off and I can see part of a green circuit board.
If the key is black, it's not a chipped key aka skim key.
The key fob only operated the keyless entry system in your case.
It has nothing to do with disabling the ignition like a chipped/skim key.
It wouldn't be the reason for not staying running in your case.
Have you been able to check for DTC engine codes with a code scanner/reader?