Will a bad timing belt cause a car not to start?
No, not necessarily. It depends on 'how bad?'
If the belt has actually broken, or has slipped a few teeth,
then it is possible that the timing is out so much, that the
pistons hit the valves and jam the engine. The belt would have to
be more than bad and actually broken.
A worn or perished belt,will still allow the engine to work,
right up to the time it actually fails.