I have a friend who has 2 of these cabs and I work on them for him. His has 3 hinges, but they are the same kind. What needs to be done is this...
1. Get the coin door open and reach up and under and feel the hinge locks
2. Pull the bottom of the hinge lock towards you and up
3. The hinges should be unlocked now, but still latched
4. The pic that you linked shows the inner parts of the cabinet.... #1 on the pic is the hinge lock, and #A has nothing to do with the hinge....if you looks closely, its a pull out panel, and #A is related to mounting hardware deep within the cab, but not the hinge. Now, where you marked #X on the pic on the back of the control panel, there should be a metal rectangle with a cutout slit on it for the hinge lock to slide into. When the Hinge is in the slit and then pulled down and away it pulls into itself and locks completely.
http://www.lizardlickamusements.com/images/for_sale/cabinets/trunk_latch.jpg
5. What you might want to do, is push the bottom front of the control panel up and forward slightly, while your other hand is underneath slipping the lip of the hinge out of the cutout slit. Thats all thats needed.