There should be a wiring diagram inside, it'll tell you which contacts in the timer should be closed when the timer is asking for heat. These will be closed whether or not the machine has power as long as it is in a position where heat is required (timed dry for instance) so look at the diagram and see if they are closed. They'll have a letter designation to ID them one the timer.

But first verify that the machine is getting 240v at the terminal block and that the hidden fuse (if there is one present at the terminal lock is not open) Flip your breaker several times if you are not seeing 240 at the wall / or terminal block. It sounds basic but it's gotten all of us a few times in our work.

Since you have heating at times we can rule out all safeties/thermos and the elements. None of them would be likely to have an intermittent issue other than a loose or burnt connector.

So that leaves the timer as the most likely issue. I'd definitely like to examine the prongs of the plug for evidence of arcing, same with the cord connections at the terminal block, either of which could cause intermittent issues. If no burns or pitting on those parts I'd say its internal to the timer. I may be wrong as diagnosis online is not easy on odd issues but you've got to start somewhere.

There is a centrifugal switch on the motor that provides L2 120v to the elements. On that pic above trace L2 to the motor switch. That's it.
When the motor spins up a pair of spring loaded weights on the inner shaft spread out and push an arm to close the circuit. If one of those springs is off or broken that would cause it. You can slide the plastic color attached to the the weights to simulate spinning but moving the switch arm is easier. The arm itself hangs out of the back of the terminal block on most motors I've seen. You can manually move it and see if that circuit closes, creating continuity or very low resistance through the switch. It looks like it'll be black to purple on the motor terminal block. That brown plastic on the motor is pretty fragile so be gentle on it.
It is a possibility. Samsung had a batch of motors recently with bad centrifugal switches and the first few I saw really baffled me.
When you look closely all that will make more sense. I'll see if I can find a good pic of that set up if its action isn't apparent when you look at it. The weights are usually silver and the springs small and attached to each weight. Its worth checking since looking is free. You'll be a GE dryer expert soon.

Well I'd say you found the problem.
We usually replace whole motor so I've never tried to find just the switch.

You might try using manufacturer data on the motor to look for parts or see if there's a local elec motor repair shop near you and get lucky, I doubt GE made it as the same brown switch is on most motors I've seen.
You'd need to cut that overheated and corroded wiring back to a good spot and crimp new terminals on or you'll be doing it again soon.
You may find a used appliance shop nearby with a boneyard that might have something too.

Nothing can be easy.

So I got the new motor in but the motor switch is different so I dont want to hook it up the wrong way. The instructions didnt give any details on the posts on the switch. It only said that the ground had to be moved to the shell.

Atleast the old switch had numbers on it, this one does not!

I have attached pictures of the new switch and the old switch pattern.