Central locking system randomly locks and unlocks doors - 1999 A4 Audi

Hi,

I have several problems with the central locking system and alarm of this unmodified 1999 Audi A4, which may or may not be related:

1. The central locking system will lock and unlock doors at random. This can happen when the car is moving, parked, or unattended parked!

1. A problem linked to the locking system occured yesterday at a gas station. I would unlock the doors, and the doors would immediately lock again (including the gas door) - so that I could not fill up the car. The problem was solved by asking someone to stand by the gas door and quickly opening it while I was pushing on the unlock button on the driver side door.

2. The remote control keys don't work, and I am unsuccessful at attempting to reprogram them.

1. The alarm system blinking light does not light over 90% of the time (it has lit only once recently).

2. The trunk lights don't work when you open the trunk. I add this info in case the problems above are caused by a malfunctioning switch detecting the status of the trunk closure.

Has anybody experienced these problems... What should I look at or test to troubleshoot the problem and fix it? I only have a voltmeter for now...

Cheers!