Rear lifgate window will not open and therefore the lock will not lock when alarm is on

It sound like the rear lock is messed up. First thing to check is the fuse in the block under the hood. Many things are fused separate. If the fuse is good you must next check the circuit by removing the rear hatch panel and insuring you have power and ground at the lock actuator. If there is then it may be the lock actuator itself or you may have the rear gate locked out of the system. If that is the case, the dealer may have to unlock it in the computer system. If it has a key at the rear gate see if you can open it manually, sometimes that will re set it.