Almost forgot to answer the question posed.
First let me say I've never had a window stuck in the closed position when the regulator cable let go. Instead I'd hear the pop and watch the window fall or I'd be headed to the Jeep and see the window was done and kick my self for being so absentminded only to find out it would not go back up when I hit the switch. Not saying your cable didn't go, as you did mention the tell-tale pop. Just never had it happen that way to me.
Once you get the panel off and remove the speaker and vapor dam, you will see I believe 5 or 6 bolt heads that hold the regulator in place. Some will be going through holes in the metal (3 if I am not mistaken) and they need to be completely removed. There will be others (2 or 3) that are located in a slot that eventually leads to a hole big enough for the bolt head to slip through. These need to be loosened enough so you can slide the entire regulator to the point where all the bolt heads go through the large holes. You'll want to put don your ratchet after they are loose and use both hands to remove the regulator. It is at all heavy but it is almost too big to fanagle out out of the opening in the inner metal panel. Putting the new one in can be even more frustrating with the cable intact but it will eventually line up so that you can move it into place and bolt it down.
Sound far more complicated than it really is and will be much clearer once you open things up and take a look.