The last time I got some horrid noises from my Jem - and trust me, the noise was driving me INSANE - I accidently discovered that there was a tiny shard of metal lodged in the
pickup selector switch. I turned the guitar upside down (so the pickups are facing the floor) and moved the switch back and forth and shook the guitar a fair bit. The shard fell out, the tone was back, I kicked ass.*
* note: asskicking may not have actually occured.
I suppose if that doesn't work, it might be worth taking the pickguard off and checking out the innards. Or take it to a shop. I found this dude online who runs a
guitar shop and the first thing he asked was: does the guitar makes the same noise on another string when you play the same note (or via a harmonic). My answer was a resounding yes! but by then I had found the solution. Now unfortunately I don't remember his name or his website, but this might have actually been a good story, mightn't it?