Looking at the schematic I see where the timer is the only thing that can keep the dryer running past when it should turn off, so you need a new timer. Secondly, There is a non-resettable thermal fuse with two blue wires going to it that can be the cause of the gas not coming on, but you will have to test it with an ohm meter. There are also some other things on the gas valve and assembly that you can test in case the fuse is good, but I really doubt you will have a problem with the other parts, however, the readings and test points are clearly labeled on the schematic near the bottom. You should test the solenoids because if they are bad, or the main one, nothing will fire. One is 1220 ohms and the other is 560 ohms. Just unplug one wire when testing something.
You also need to totally tear it down and scrape out and wash all of the parts except the motor, which you vacuum out. You can go to YouTube to see videos on how to take it apart, but do a very good job or it will fail again quickly. Dirt makes the fuse blow. I would get a new belt and change it while you have it apart and get some white lithium grease and grease any bearings you find. You need to clean out a drier every two years, at least, according to the manual. All sensors work together by comparing temperature, so all need to be cleaned. You just unplug the wires from the sensors and remove ductwork that they are attached on and clean the entire thing with soap and water. Make sure you go all through the dryer and get all parts like the blower fan and housing, vacuum out motor well and clean exhaust. Mark all wires you unplug so you know where they go. This is an easier job than you would think. My sister does hers at least once a year since she has five children and the dryer gets a lot of use. This is an easier job than you would think. See:
Dryer vent cleaning prevents fires - YouTube and:
Cleaning out a dryer with top lint cleanout - YouTube
Cleaning out a dryer: By a woman 2 of 2 - YouTube Make sure to clean the exhaust and that ductwork and outlet on side of house, too. Your dryer should last a long time after this if you keep it clean.