There can be a number of causes for the symptom you describe. The first thing to check is the fuse for the circuit to the heater. Another potential issue is the thermostat which may not be triggering properly. If the temperature setting lever is set all the way to the right (highest setting) the small metal contacts inside may not be touching; thus no start signal.
The most frequent failing part is a bad "sail switch" ('air flow/limit switch fault' an override that ensures the blower is operating).
Here is a link to the troubleshooting manual for techs:
http://bryantrv.com/docs2/docs/hflamefurn04.pdf