Right, I have a Peavey Vypyr 15 and an Epiphone Les Paul Standard (yup, seems like pretty stereotypical gear :p)

Anyway, whenever I turn my volume knob high, or my volume knob low, I get quiet, but audible high pitched noise whenever I play a note. There's no noise when idle, only when a string is struck.

I've tried changing cables and that didn't work. There's no noise when the volume knob is on full or the tone knob is on 0. (I've also tried searching this up, and something about grounding has come up?)

Has anyone had this problem before? If so, what was the solution, was your guitar at fault or the amp?

Have you checked to see if the guitar is to blame? I guess on my first pass through your post it looked like you didn't swap out guitars. I would do that. Sorry if that isn't a help.