First, you might try a volt-ohm meter... even an inexpensive one at a ten dollar price range will tell you anything you need to know. It works better than the old tongue test, which, at weld current levlels, might be a bit excessive of a tingle and could tend to curl or even smoke your hair.
Second, without sounding heartless, rude or cruel I would like t comunicate to you the need for me/us to evaluate your level of training, experience and your capability to perform a safe, dependable repair on your equipment... If you dont own the test equipment it's not a big issue, but it's certainly an indication, if you don't know how to use it either, that you should perhaps send it out for repair...
...this site does indeed provide a lot of information, but it might be necessary to get a level of formal training in the basics first. Take it under advisement and think of safety above saving a couple of bucks.
I have never seen the wire feed unit you describe but a generality or two might help. First, I'd try to find SOME point on the power supply that does read weld voltage (on a VOM[meter]), tracing back from the contact tip of the gun through the wire feed system right on back to the inside of the power supply itself if need be, bearing in mind that the ground side of the circuit is as critical as the "hot" side. Somewhere you should find a connector or point that does show power, or it would suggest the welder is bad. Check your power at the outlet first before going any kind of nuts... read the voltage on the VOM to be sure. A continuity test of the gun from the contact tip to the machine connector may be confusing if there is a contactor or relay as I would expect. Work systematically and use logic; don't guess and jump around haphazardly.
It would be unwise to begin replacing parts without knowing howto test them first; just because power may stop at a relay does not necessarily mean the relay is bad... post any new questions
Finally, I have no idea of hourly rate or hours involved to fix your machine, so I am unable to comment on the second part of your question.
Good luck and regards,
d