My LG Tromm detergent door is stuck closed and I can't get it open.

Here's what I would do:
Take the two screws off the back plastic parts which are attached to the top cover. Leave the ones in that go into the cover, just remove the bottom one on each side.
Now, standing in front of the machine, use the palms of your hands to sharply push back the top cover (pushing on the right and left edge of the top). It only moves about two inches. Now, lift the cover off.
Use a flashing to try to see into the semi opaque dispenser to determine where the hang up is.
Drill a small hole in the top of the dispenser chamber to allow you to poke an object like a screw driver in to manuver the offending part of the dispenser, allowing removal of the dispenser drawer. Use a peice of foil duct tape to seal the hole you previously drilled.