I too agree that a professional groomer or a vet needs to shave the cat down. Cats have very thin skin and someone without cat grooming experience shouldn't attempt it.

I also wouldn't bathe the cat. A bath will cause the mats to be even tighter than they already are. A conditioner will do nothing when the mats are bad. Conditioner works well on tangles and sometimes small mats, but usually bathing makes mats worse.

Do you have a low cost vet clinic near you? Usually humane society's have low cost vet care and check-ups. That would probably the best place to start. They could probably shave him there. I know groomers are expensive when it comes to cats.