That sucks. Too much noise drives me insane. I've been playing my LP for about the last 3 months. Yes, the tele has been neglected. With the humbuckers, a tube amp and 9 pedals (ran off a one-spot) I have no noticable noise. Take the pedals out of a chain and try them one at a time. You may find the culprit.
I'm sure someone on here knows so much more about this than me. I just know how aggervating it can be. Sorry I can't be of much use. Good luck.
There's fever in the funkhouse now. - Mick Jagger