Yeah the guitar your descirbing is very obviously the typical Les Paul arrangment which is famous for not being noisy (unlike my preferred weapon of choice the strat)...I would say at a guess it sounds more like (assuming that you do have your wiring and soldering skills up to scratch that you have a cheap set of pickups which may well have become very microphonic and have lost their power....your best bet may be to beg borrow or steal a spare pick up and wire it in...if it works ok then you'll have to go for new pickups (i'd recommend EMG's or Seymour Duncan's) if not then you could some new pots and selector switches along with new wires for the lot.....failing this take it to a Luthier for a good ol' overhaul and he'll set it straight.....if you want more info repost with some more exact details and i'll be of as much help as i can!