Does the motor hum like it's trying to turn? Check for lint build-up in the motor area. Sometimes the motor switch can become blocked open by lint. [COLOR="Red"]Don't do any work around the motor until you have unplugged the dryer[/COLOR].

The motor has a mechanical switch built into it. It used to be a replacable switch, but now it is an integral part of the motor. It has two functions. At rest, it closes contacts between the motor start winding and neutral. When the motor ramps up to speed, centrifugal force opens this contact, dropping the start winding out of the circuit. At the same time, this centrifugal force closes contacts on the same switch between the heat circuit and neutral, allowing the heat to come on. This is designed so that no heat will come on until the air is circulating in the dryer.
Sometimes lint build-up causes this switch to remain in the "run" position, causing the motor not to start, but allowing heat to be energized. This will eventually burn out the motor run winding as it attempts to start without the aid of the start winding. It can also present a fire hazzard, with the heat being activated without ventilation.
This may not be your problem, but it's a good place to start troubleshooting. Just unplug the dryer, open it up and vacuum out the motor unit as thoroughly as you can, and see if the dryer will start.