First thing is to check the adjustment of the switch location. It can be raised or lowered in relation to the brake pedal. If that doesn't work, then you need to remove the brake switch, take it apart, clean the contacts, reassemble, and reinstall. Different switch but should be a similar solution:
Car won't start!...and it's not the Steering Lock...
Or you could probably buy a new one. I don't think they're terribly expensive.