There is a piece of plastic (circled in image provided by boofoo) that commonly breaks. In the same diagram, see the part just to the right of the circled plastic piece? That's your clutch safety (interlock) switch -- when that switch is NOT pushed in, you cannot start the car (this is a safety feature and also the reason why you need to press the clutch in to start the car).
When you press the pedal down, the plastic piece pushes against the clutch interlock switch - then you can start the car. Without the plastic piece there, that switch doesn't get pressed in, so the car won't start.
Replace that plastic piece (like $3), and this should resolve your issue.