According to Appliance Parts Pros, troubleshooting a gas dryer begins with determining what the problem is. Problems usually involve the igniter, the coils or the flame sensor.
If the dryer starts its cycle hot and ends its cycle cold, the problem is likely to be the coils. Older coils degrade and lose their ability to keep the gas valves open. This can lead to the valves opening and closing at an accelerated rate, which produces a chattering sound. Appliance Parts Pros advises that there is no way to test the coils, which makes replacing them a larger decision.
If the dryer never gets hot, examine the igniter. Disconnect the clear plastic tube that attaches the igniter to the burner. Next, place probes on the contact points of the igniter and measure the Ohms of resistance. If it is over 100 Ohms then the igniter needs to be replaced. If it is under 100 Ohms, test the flame sensor for continuity between the two contacts. If there is no continuity, replace the flame sensor.
If the preceding ideas did not fix the problem with the dryer, examine the burner for a build-up of lint. Lint may block the flow of gas and keep it from igniting.