The fact the pump runs for so long is your first clue. I have never experienced this, but apparently there is a sensor in the pump that detects the rise and fall in pressure/vacum to determine when all locks have completed moving. I have a bad pump here at the house, and I found the diaphragm in it that appears to be this mechanical sensor.

This implies to me that you have a lock that is defective/damage, a hose fallen off a lock somewhere, etc. I'd suspect the door you mentioned. WHY this would happen, I sure don't know, it should not be a problem. THe fact that all locks work but the one leads me to believe the pump is OK, and it's the lock in that door, disconnecting and reconnecting the battery, in my mind, is not related. Sounds 100% mechanical to me.

IF you can determine which line from the pump is that door, you can disconnect that line, plug the linen with you finger, and have a helper activate the locks. If the pumps acts normally and runs 2-3 seconds and all other locks work, then you know it is that one line or lock.

The manual claims that the passenger lock is operated by the same line as the trunk latch lock. Does the trunk REALLY lock and unlock? If not, that would also point to a big air leak in that line, caused by a goofy lock or broken air line.