Extruder motor not running during print job but working after I preheat the extruder and test it
According to all the information:


No reassignment of the extruder in the Gcode
You can extrude if you push the filament by hand
Extruder motor works when switched to Z driver
Z Motor works


I come to the conclusion that some of your electronics or the motor have fried.

What have fried? I tried to make a step by step check:

Switch drivers between E and Z, but plug the motors as usual:

1) Does the extruder extrude?

Yes: Your driver has fried

No:

2) Were you able to move the Z motor?

No: Motherboard And driver has fried

Yes: 

3) Plug in the E motor on the Z driver, can you make the E motor turn?

Yes: Motherboard fried

No: Motor fried

HTH and keep us updated if it worked or not!