The car battery died and I was waiting to get a jump and I noticed I could not unlock the car with the key fob and then I stick the key in the door to try to unlock it and the lock is just freely moving back-and-forth. There is no engaging with the key in the locking mechanism. I replaced the key fob battery key fob will still not lock or unlock the vehicle, so I am thinking it is the lock itself or could it be a blown fuse from when the battery died and was jumped?. Does anyone know how I can test the theory for the fuse, or for the locking mechanism?

 

There is no direct connection from the key to the lock - it is all actuator operated and the key only turns a switch.
If you have a dead battery you need to connect jump start positive to the starter (from underneath) and then you will be able to open the door.

 

The car has been jumped and it starts. The key still is freely moving in the door.