My gas oven will not turn on in bake or broil mode. Since it is apparent that the control buttons and gas lines are working, my first guess would be the ignitor has weakened to the point where it is no longer able to send a signal to light the burner. The ignitor needs to be taken out and tested for continuity.
Step 1: Safety First
Pull your oven gently from the wall. Shut off the power by unplugging it and then turn off the gas.