There are a few different reasons that can cause the gas burner to not light.
Following these steps may diagnose the problem.
During normal operation with the burner operating correctly, there are a few sounds that can help diagnose certain problems. Normally, when the thermostat is turned up, the burner blower will begin blowing air into the firebox and about 40 seconds later, the gas valve will click and the igniter will buzz. If the flame does not light, the buzzing will stop after about 5 seconds and the ignition process will stop. This will not repeat unless the thermostat is turned off and then back on.
If the burner blower does not start blowing, nothing else on the burner will work. If this is the case follow the steps to diagnose a faulty thermostat or a Hi Limit that is tripped.