There are just a few possibilities...
1) Power supply. There has to be power to the control board. (Fuse?) Test with voltmeter.
2) The control switch & wiring to switch. Test with ohmmeter.
3) The motor & motor wiring. Test for appropriate voltage to motor with voltmeter. (Most are small DC motors up to ~12v)
4) The feed rate control. A potentiometer (Variable resistor) & wiring. Look at it, usually a broken solid wire due to vibration during shipping. (Actually could be any wire to/from control board) Can test with ohmmeter.
If it's in the control board, the major component is the SCR, a 2$ replacement at radio shack, much better than a $150 board! Fixed 2 of them this way, they are damaged by power surges!
Ussual blow your fingers off, not my fault disclaimer; You expose yourself to death, disability, causing more damage to your equipment, scorn of your spouse if you let the smoke out, etc, etc, etc, anytime you are working with electricity. Seriously, welders are capable of serious current & can cause great damage to you & yes, even death. Be careful!