2006 jetta trunk actuator switch won't work - 2003 Volkswagen Jetta TDI

No button is available you must buy the whole switch or "Jerry rig" them with some other knob from Radio Shack

FIRST: try using the gas release lever from inside the car with the driver side door closed. My 2006 Jetta gas release lever would only work if the driver door were shut and I pulled the release from the inside car interior. Turns out it was a severed door wire (NOT THE RELEASE CABLE). Thus when the door was open, it stretched the damaged wire and so none of the door controls worked unless the door was closed. ie windows, trunk release, and gas release. It was a $600 repair at the dealership, parts and labor! :(

There are 3 phases to fixing your car's trunk lid release problem.

Phase 1: First check the fuse - once you know that's OK, then proceed to phase 2 (below).
The fuse for the trunk lock is
the bcm (pwr) 15A fuse in the instrument panel fuse box (behind panel at drivers right foot)

Check that fuse, as it is the power supply for the button on the dash that sends power to the actuator in the trunk.

Phase 2: Get the trunk open (without taking it to the dealership).
If you have remote keyless entry to the trunk, you could try that - but with the actuator
dead/dying, it shouldn't work.

Here are a couple of ideas to try to enter trunk while (a) actuator isn't working, and (b) all
valet lockout features (designed to deny valets access to the trunk) are in the "Lock" position:

There is the lock cylinder, which you stated is not functioning - put the key in, and it doesn't
turn. Just to be sure, consider: lubricate key with Graphite lock-type lubricant, and retry.

The trunk has 2 valet safetys...the locking rear seats which require access to the trunk to unlock, and then there is a valet switch in the trunk that locks the button on the dash from working to keep valet parking attendants out of the trunk. That may be in the lock position.

You can try accessing the center area of the fold down rear seat and see if you can unhinge the rear seat from there. Maybe reach in with your hand, or an extension-type tool.

there may be a way to fold the hinge away from the seat back so it can be removed from the hinge and give you access to the safety latch in the trunk and open it that way (white handle in trunk).
The white-handled safety latch release is desiged to prevent accidentally trapping children, and
if you can pull it with your extending-type or grasping-type tool, the trunk will open whether or
not the actuator motor is working.

Phase 3: Replace the Problem part.

Your failed part may be either (1) Trunk Release Relay, or (2) Trunk Lock Release Switch

My Satrun ION manual doesn't cover either of these parts, and the online parts houses, e.g.
http://www.rockauto.com/catalog/x,carcode,1431624,pgname,Electrical-Switch%2B%2526%252338%253B%2BRelay,a,search.yahoo.com%2BSearch%2Bfor%2B2004%2BSATURN
fail to provide instructions. One of those times a mechanic has to t=rely on his/her native
handiness and/or experience.
To identify which of these parts is bad, locae the Trunk Release Relay (call your dealer parts
dept. for helpful tips on finding it), then operate the dashboard trunk release button with your
ear close tothe relay - if it makes a noise, the problem is the Trunk Lock Release Switch in
the trunk lid, otherwise its the relay.

Crawl through the rear seats and remove the trim panel with a Philips screwdriver. Most likely the actuator rod has come off at the lock mechanism. Once the trim panel is off you will be able to open the deck lid by hand.

This is a clue, not a solution. It happens with my 1998 Jetta GT the same way, same delay. The condition comes and goes intermittently, and seems related to the trunk lock. There's a switch operated by the trunk key lock. I think that's where the problem lies. I can go for days with no problem, but sometimes after I have opened the trunk, when I lock the car the alarm goes off a minute later. Nothing will change it except opening and closing the trunk, but not every time.

the contact switches might be sticking,chech fuse contacts are clean and tight

How to Repair Trunk That Won Open part 1
How To Install Replace Trunk Latch 2006 12 Chevy Impala

you need to remove the trim cover on the inside of the trunk lid. it sounds like the solenoid is jamming. the solenoid should flick out against a lever that will release the trunk lid and then return back again within a split second. if it stays out then it is jamming, and thus holding the truncks locking mechanism open.
the solenoid may also jam shut and therefor not release the lock. if you can see this happening then replace the solenoid.