Update: the front panel comes off, but now I can't get access to the broken latch.

Vroom, I hear a chain saw in your future!! Al kidding aside, can you access the hinge screws/bolts? You might be able to work it apart that way. If not then I would suggest trying to remove it from the opening and maybe take it in somewhere to repair it. This would be a good time to have that in house warranty at hand if you have one.