Firstly, make sure your vent is unobstructed from the dryer to the outside vent hood.
Check the vent hood itself to make sure it has not been crushed. Venting should be cleaned/inspected twice a year and kept to a minimum length without 90 degree elbows or pinched tubing.
The most common failure are the gas valve coils, but read on from an excerpt at; www.repairclinic.com
If your dryer doesn't heat, check these:IgniterGas valve coilsThermal fuse
Modern gas dryers use an electric igniter to ignite the gas from the gas valve. When it's working properly, the igniter glows bright orange. When it burns out, the dryer tumbles but there's no heat because the gas can't ignite. When the igniter burns out, you need to replace it. If the igniter is held by a tension bracket, you very well may need to replace the bracket too.
The igniter is inside the dryer housing, near the bottom front, usually in a cone-shaped metal tube (the force cone). It's about 2 inches long. It's mounted to the far end of the burner tube, and it has two wires attached to it--or to the tension bracket, if there is one.
Gas valve coils
Watch the igniter. Does it glow bright orange, then shut off without igniting the gas? (When the gas ignites there's a large blue flame.) If so, there may be defective coils on the gas valve. Mounted on the top of modern gas valves, there are black electrical coils. The coils, when energized, open the gas valve. If one or more of the coils are defective, the valve doesn't open and the gas cannot ignite. Because it's often difficult to properly test the coils, it's usually best to replace both (all) of them at the same time.
On many dryers, there's a thermal fuse (a heat-sensitive fuse that blows if the dryer overheats) mounted to the exhaust duct inside the back cover panel. The fuse is about an inch long. It's usually embedded in black resin and mounted in a white plastic housing.
If the fuse has blown, it has no continuity. When this happens, your dryer either just stops heating, or it doesn't work at all. Be sure to inspect the venting/heating system before replacing the fuse to put the dryer back into operation. (You can't re-set this type of fuse.)