Hey Martin, I had a similar situation on my 92, not sure if the 2002 is the same. On mine I had to depress the button and pry the lid open. The latch had two little ears that retract and release from a thin metal plate mounted to the body of the compartment base. One of the ears was not retracting. I took the latch out and found that something had broken in the latch itself. This left me three choices, (1) remove the plate held in by two screws and have to no latch at all, (2) replace latch $$$$, or (3) trim the metal out of the plate that the side of the latch which was no longer working used to hold on to. For my 92 with 250k miles #3 made sense and worked for me. Again not sure if this works the same on the 2002 but maybe it will give you an option or two.
Good Luck
Best Regards,
Tony