its either 1 of two things, when u pressed extra hard on the brake pedal you busted a leak in a worn brake hose,that would explain the brake light turning on b/c there is low brake fluid, or your brake master cylinder has gone bad. check under your car and especially around all the wheels, b/c if it is a hose, its prob 1 of the rubber ones that go to the wheels. if u dont see and brake fluid leaking, with the car off push the pedal with normal pressure and hold it, if it slowly goes down, its the master cylinder