The resistance is printed on it, read this and measure across the leads with a multimeter. Don't be surprised if there is some difference because it is in circuit, but if it reads more than 10% higher than what is printed on the side that's bad.
Can you qualify your statement?
If the component is in the circuit - and it would be until one leg is disconnected from it - the resistance value is anyone's guess without knowing the details of the circuit in which the component is placed. Therefore, placing a blanket "10%" value on range of resistance from the marked value to be "bad" if outside of that range I think is a WildAssGuess. I would be curious on the reasoning you have for the "10%" value if you do have sound logic for it, however.
For the original issue - I see that board uses through hole components. That makes life easier than surface mount components. Those boards are relatively easy to work on that way - if you have some patience and steady hands I'm sure working on the board can be done. There are ways to repair broken traces and pads if you screw any up, however what you have to be really careful of are multi-layer boards with plated through-holes. Sometimes boards will have 2-4 layers to them and what connects circuitry between the layers is a sleeve, or plating, inside of the hole that a component lead is soldered to. If you aren't careful with your re-work and you pull a sleeve through with the lead of a component you are removing you are loosing that component's internal connection to the other board layers. That is pretty much a catastrophic problem because you can't open the board layers to expose the disconnect where the sleeve was originally connected inside.
If the board is single or dual layer (top and bottom traces, no layers sandwiched between) board re-work is a lot more forgiving.
The IC's on the board can be sensitive to static etc. If you have an IC that is part of the variable speed drive for the wire feed circuit that is bad this could also account for the problem. A lot of times those IC's are very run-of-the-mill components and can be had on ebay for pennies. Sometimes, if the circuits that components are in are old - even within 5 years, you can find certain components obsolete and no longer produced. In that case, you may need to find the original specs of the component and see if there is a current production component that is the same or close enough.
I have a ham radio that had a component issue once. It is a kit radio and the manufacturer was unable to source a particular IC as a through-hole component. They were able to get it as a surface mount instead. So what they did was they built the surface mount component on a "daughterboard", a micro-size circuit board about the size of a penny, that had through-hole IC pinning on one side to go to the main circuit board, and the surface mount IC soldered to the other side ready to go. Pretty slick solution.
