It sounds like it might be sticking.  Scotty has a video on it. 

The plastic runners in the window assembly are notorious for failing. Basically, the plastic gets brittle, cracks and fails with age. The window will generally move only in one direction or not move at all. If you are paying attention when lowering the window you'll hear the cable crunching up the plastic runners. The cable gets hung up in the broken assembly and can't unspool to let the window go back up. 

I've had three window motor/regulator assemblies replaced just for that reason on two different Crown Vics. All of mine failed while the window was going down.

Those assemblies are riveted in. You can drill out the rivets and replace with either 8mm or 10mm bolts (I can't remember which); just be careful because at any step of drilling or tightening the new bolts and you bust the glass. Of course, the dealer can do it for you. 

To get it back up, the door panel comes off pretty easy. One hex bolt behind a the pull handle (remove a little square cover). Pull off the window switch panel and you see one bolt to remove. Then depending if a front or rear door you'll have two bolts at the very bottom of the panel. Then just lift straight up and off. It's actually very easy to remove and if you've done it often like me you can do it in 5 minutes or less. Then just look inside the door and see if you can lift the window by hand. If it won't move by hand, you can just cut one of the cables, push the window up. I've used a binder clip to temporarily hold the window in place.