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Would suggest this first, as least invasive. Regards the pots being quiet, the De-Oxit may clear that up.
If the guitar was purchased new, you have certain rights that allow repair to be made by PTC, at cost less than a local tech could do. If the guitar was purchased used, then best to try the local tech.
What you can do that will not void any warranty or do any damage to your guitar is check out the wiring and contacts with the multimeter for continuity. You may not be able to check the capacitor's continuity (and I'd strongly avoid doing so) because it might spike your multimeter. Not saying it will. Might. If possible, also check the output jack for continuity.
With the results, you'll have a better idea of what to say to either a tech or PTC.