Well, I talked to my brother, and he said that when his Celica had problems (I guess it didn't quit, though), it was the timing belt. It had jumped a cog, and so still ran, although quite rough. If you never noticed it running poor before, or it didn't just quit on you, then it's probably not that. The timing belt is one thing, though, that is supposed to be changed regularly. I think about every 100,000 kilometers, or about 60,000 miles. Quite often, the timing belt never does get changed until it wears out and breaks, causing other engine damage.
I doubt that's your problem, though. I would say it's electrical or ignition related.
Are you going to have to get someone else to fix it, or do you try to do what you can, yourself?