Back door wont unlock

I have a 1999 Chrysler T&C 3.8 liter like yours and it sounds
like you are having the same the same problem I had.
Every time you hit the door unlock or lock button, it made a loud
buzz like you just missed a question on a game show. ;-)

It turned out the problem was the rear lift gate lock actuator. The part costs
about $40 from the dealer if I can recall correctly.

The repair involves: 1st removing the middle and rear seats to get
access from the inside to the rear gate
(obviously you will have to remove the seats from the side doors
since the rear gate won't open yet)

Remove the plastic inside rear gate panel and molding (phillips screws)
Once you remove the panel, you may see a way to manually
open the rear gate. As I recall, I think there was a access opening
covered from the inside with a black weather/insulation tape.
Carefully removing this out of the way gave access to a way to
manually open the gate, making the rest of the work easy.

Remove the electrical connector and the mounting bolts
to remove from the actuator. It is attached to the inside
rear gate with 2 or 3 bolts (10 mm?)

Remove the old one and replace the part, then put it all back
together, make sure you reconnect the electrical connector

Takes about an hour for the whole job (max)

Hope this helps,

Wes

Sounds like a bad door lock actuator.