Sounds to me like the lock is jammed somehow. If the door is locked and you pull on one of the handles, there would still be tension (of course, the interior handle unlocks and opens the door, but you get the idea).
1999 Cougar, Laser Red, 3.0L V6, MTX (a lot more fun)
2014 Ram 2500 Big Horn 6.7L Diesel (Towzilla)
2012 Honda Accord V6, ATX (daily)
sorry for my absense but i am a Master Tech please listen to me. lol. check out my door panels i have all kinds of door panel experience.
remove your cougar head, remove the screw in the hole, and theres another in the lower left carpet, which is definetely gonna suck with the seat being there and just pull the panel. im tellin you, the side torx bits screw into these plastic clips that push into the inner door structure. these clips are available at a mecury dealership no problem and they're very cheap. i promise it wont be bad. my only concern is the access issue with the lower left screw. it may make my plan not work.
Got it open, thanks all. Took CougarGuy's advice and popped the panel loose. Had to fold the panel back for access which was kinda ugly but looks ok when laid back in place. Also had to cut out a section of plastic under to get at the latch mechanism. It wasn't fun getting it out (the word "cluster" comes to mind) but as I suspected the problem was in the latch itself. All the linkages and the remote keyless connecter were hooked up and working properly. A slim jim wouldn't have helped. I had to persuade the latch itself to open with a screwdriver. The only problem I could find with the latch was that the piece which engages the pin to hold the door closed, is coated in plastic which had a small nick in it. This seemed to cause the latch to hang up and not fully disengage. I trimmed the plastic smooth, thoroughly cleaned the mechanism, and lubricated it with graphite powder. I can't get it to stick now. I'll try to get some pics before I put everything back together.