The door latches on my convertible -- doors nearly identical to the coupe --  
were dirty, causing the window to not drop and raise as the door was opened
and closed.

The trouble was the linkage inside the latch. I opened the latch and
cleaned, and used a bit of sandpaper, and was able to get normal operation
again.

You didn't say where you live, but cold would play a role in this problem.
If the door(s) worked oddly last spring ans summer, then it stands to reason
they would not work well at all this winter.

You can monkey around with the latch -- simulate the striker post by using a
nutdriver or equivelent -- and see if you can get it to free up. Press the
tool into the jaws of the latch, or use your finger if you want, and make
the latch lock. give it a shot of spray cleaner and some light oil, and
repeat. Operate the door latch to open the jaws, then close the jaws again.
There are small parts inside the latch though, and you probably will not be
able to get to the switches and thier linkages from the outside.

Perhaps you can get the door handle to cooperate without taking the door
apart.

Firstly, lube the door catches with grease.