Key will not come out

Check your battery voltage first. If it tests good then check the fuses for power at both ends with a test light. You will want to check fuse PWR MOD (2 amp) in the panel at the right side of the dash, also the 10 amp air bag fuse and the RV C Sensor fuse in the under hood block. All of those feed the theft deterrent system and shift interlock.
If they are all good and the battery is good then it could be the BCM. But I would have a scan tool put on it first to be sure.

Under the dash to the left of the steering column. But it is not a plug and play item, any replacement will need to be programmed to your vehicle for anything it controls to operate, not something most places can do as it also involves the security system.