Stuck Space key, huh? First, see if the key is physically stuck in the "down" position. Sometimes some sticky crud or whatever can get stuck under a key and hold it down. Otherwise, you can replace a keyboard for around $12-15.00. Not too bad.
It's keyboard replacement time. The controller chip inside has most likely fried. They're cheap, though, like $12-15.00. One word about this: You need to determine (if you don't know already) whether you have a PS/2 or an AT-type keyboard. The plug on a PS/2 keyboard is about the diameter of a pencil head. The plug on an AT keyboard is about the diameter of a dime. Of course, most of the ones you buy these days are PS/2, but include an AT adapter if needed. Do not, under any circumstances, unplug or replug the keyboard while the computer is turned on. That can actually damage the keyboard controller on your motherboard. Good luck!