Good news on the locking....I think you have a vacuum leak.
The vacuum should have enough pressure to lock and unlock doors, trunk and gas tank 3 or 4 times. Then you need to start engine to re-pressurize system.
I would work from the driver's door to test the system - as that is the master lock on the car.

Not sure about your year, but do you have an alarm on the car? Could have been disconnected and that COULD be part of problem with locks.

I would start trying to determine if you have a vacuum leak. Look around the tank first - look for any deteriorated rubber connectors, anything around the door hinges (hidden by the rubber boots).
good luck!