Check your control configuration in the Setup menu in game. Whatever you set the "USE" function to (not to be confused with "Use Item") that is the key you should be pressing while touching the appropriate activatable panel/button.
You don't actually "use" the Supply Key. Like other keys in the game, you merely have to have picked it up, and then when you try to activate/open the door or button that required it, it should open/activate.
If you are really confused, there's a complete walkthrough (mind the spoilers) at the Strategy link in my signature (just click on the link in the sidebar on that side to go to the Jedi Outcast section and you'll see the walkthrough link).