might be the timing belt...?
A friend of mine has an 89 celica which died while he was driving. It restarted and ran for a few miles and died again and would not start. We checked wires, fuel pump etc. I then checked the timing belt by pulling the upper timing belt cover to the side (I was initially too lazy to remove the belt covers completely) and the belt looked fine. However, when we removed the covers completely later on, it turned out to be the timing belt - it was really worn but it was still held in place pretty tightly - it just wouldn't turn properly.