I have a spare 6581 - 3083 - that sid was tested, but the machine gave up ..
I am however afraid, due to the lot it came from it is 10 eu inc shipping.
I would advice you personally to source a complete machine for a very reasonable amount so you have spares. Well if none available have a look at my offer.
People often come to conclusion that SID on C64C is faulty if sound is missing. But in 99.9% of cases, problem is with 9V AC power.
So check 9V AC from psu and PSU fuse first.