Here is your parts breakdown
GE DX2300EB0WW
Sounds like you shorted the resistor
Usually this is used during auto dry cycles, it reduces the 240 volts from the heater to 120 volts for the timer motor. When the heater shuts off the timer now gets voltage and advances. In timed dry mode a different set of timer contacts provides 120 V to the timer and it advances
When you shorted it out you placed 240 V across a 120 V device therefore the breaker blew also there is a good chance that it blew the timer motor's winding.
Best way to check this is with a meter.
The thermal fuse is under the dryer's lid on the heater assembly not in the console.
Could you describe "when I turn the start knob the dryer tries to start up however it stops" a little better. Does it just hum, does the drum turn, if you retry it does it do the same thing etc.?
By the look of it you have a belt break switch so this may be turning it off. Try rotating the drum by hand should rotate fairly easily. The belt tension may be changing for some reason causing the switch to open.
The motor has a thermal protect built into it, so if it does not start (just hums) it will overheat, the protect opens and it will take a while to reset so the unit will seem totally dead until it resets.
I do not have a wiring diagram for this unit so troubleshooting is a little difficult.
Usually the motor startsup when it reaches close to operating speed a centrifugal switch on the motor disconnects the start winding so only the run winding is in circuit through a set of timer contacts. If the run winding is open then the unit would stop even with the start switch closed as it is out of circuit.
Could also be a bad door switch, switch opens when the dryer starts to vibrate.
But would not expect this to be as reproducible as yours is. Try holding it closed and starting the unit
Hope this is of some help, here is a good site with dryer repair help
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PS: If the motor is shot, may be advisable to look at a new unit especially if the timer is also gone.