Seems jammed or broken. Neither the key nor the interior handle will open the door.
If the door opens from the outside handle, open it and remove the door card. The most "likely" culprit will be the rod(s) connecting the interior door handle to the latch assembly. The latch assembly itself can have problems, though.
If the door won't open from either the outside or inside door handles, this will be tougher, but not unsolvable.
If you know someone who is very good with a "slim-jim," they may be able to open the door for you without trying to remove the door card with the door closed. But they need to be very good, or else they can do a lot of damage to wiring inside of the door.
The door card can be removed without opening the door. But, this is not a pleasant job, or for the faint of heart, or large of size. In fact, if you have access to a mechanically inclined twelve-year-old, have them remove the door card.
You will need to move the seat fully to the rear and adjust the height as needed to get behind the bottom edge of the door card. If you have a tilting steering column, tilt it full-up. After this, generally follow the procedure in the service manual, adjusting the procedure as needed for the door being closed. You may need to shear one or more plastic locator and retaining pins to get the door card off, particularly at the front upper edge where the door card is up against the side of the dash board.
You may still end up destroying the door card in the process, so the slim-jim is the better alternative if you can get it to work. However, if you can't open the latch with a slim-jim, taking a chance of needing to replace a door card is preferable to the certainty of damaging sheet metal.
With the door card removed and the latch assembly exposed, you can open the door. If the latch assembly is completely jammed, you will also have "better" options on how to remove it without damaging the door itself.
While it should go without saying, do not close the door after getting it open until the door latch assembly is fixed.
Good luck, and please let us know what you end up doing to fix your door.
It might be the latch assembly itself freezing up. I don't have the manual for your Town Car so I can't say for certain.When it got a little above freezing the door worked fine. I've dealt with plenty of frozen doors but the symptoms this time faked me out. I just hope that it's not the mechanism inside the door that's freezing.