Back door will not lock or unlock when using key remote only front passenger side and back drivers side opens with remote

A plastic clip that holds the lock linkage is probably broke or worn. You need to pull of the inner door panel to see whats going on inside. Use the remote and see whats happening. It could be bent rod in door from someone using a slim jim to unlock it when they locked the keys in it at some point. Bend the rod and try the remote again untill it works properly.

change the batteries in the remotes

1) Key turns but dose not unlock door. This means that the rod that goes to the back of the lock has came off. This also means that is the reason door is not unlocking with the remote as it pops the lock rod inside the door which pushes the lock open.
2) Key does not turn lock at all but works passengers side door. This means that the locks has been changed in the door, but that doesn't sound like the problem as you say the remote doesn't open the drivers side door so more than likely the rod has came off the back of the lock

this is a problem that can appear after your car battery died, cause the car didn't reset propely, so taking the battery out and putting it back in or letting your car die again would do the trick. I tried a lot of reprogramming procedured for my remote key, none of them worked, what did the trick though was simply unlocking the doors via the all door unlock button on the passenger side door, so simple.

faulty master switch ..replace

looks like car has other issues as well.. but try that first

door lock actuator might be faulty or bad electrical contact
take off the door panel and diconnect and reconnect the wiring, you might need to change door lock actuator

If remote locks and unlocks driver door but does not unlock passenger doors,then follow the advice above:
Get in the car using the key to unlock the doors. From the passenger side lock and unlock your doors using the button on the passenger door. Get out and the remote should now unlock all the doors with 2 presses.
Worked perfectly for me after several other suggestions (and dealer) failed.