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Are these a factory fog light setup or aftermarket?
Well If you are up to it I can try to help you diagnose the problem
The very first thing I would do is check for power at the fog lights (even though the bulbs are ok)
next I would trace the wiring back to the relay and make sure there are no breaks
Also when you have the engine switched off, the headlights switched on and you switch the fog light switch off and on can you hear a clicking sound from the relay?
(you mentioned there are some snipped wires somewhere, can you see both ends of these and possibly trace them back to their origin)?
Are you able to do the other things I suggested?
I'm not sure if I can help you otherwise
I hope i'm not causing you too much hassle and I am happy to open up this question to other experts if you would prefer