To be honest, you don't even need a PIC for this type of project. Press a button to open the door, this latches and powers a standard motor, with say a rack and pinion system to move the door. At the end of the track a simple switch un-latches the switch and the motor stops. Same could then go for the closing of the door.

One area where a PIC would be useful, would be for sensors to detect if something has jammed the door, or if it was closing and someone was in the way (such as the IR detection on lift doors)