Check your connections to the jack and pots by opening the little cover on the back of the guitar. One of the wires is probably broken or making a bad connection.

if neither pickups are not responding then it is likely the jack broke. take it to a guitar shop and they should be able to put a new one in for like 20$ (or at least i hope it wouldnt cost more than that).

could also be a pot went out, do you have a single master pot on your guitar? still shouldnt cost very much at all.

i doubt any wiring went bad, its hard to mess up wiring unless you constnatly open your guitar and mess around with it. if it was a squire.. i would have said differently though.

Epiphones from Korea are notorious for crappy jacks.Get a real Switchcraft jack installed (like Rider said, about $20-25.00, unless you're out in Cali-land...) and rest easy. Which SG did you get? I have a "real" 66 Standard and the Epiphone my son just got is pretty darned nice compared to it!

Guitar's that quit working are always fun for smashing on stage. :shock: :D :lol: :x :roll: :twisted: :evil:
Or lighting on fire. And smashing up your gear.
But seriously, it def. sounds like the jack or the wires inside the guitar.
Good luck.
Have you opened it up yet?

also make sure your strings arent going on strike. sometimes guitar strings will go on strike if they are played too hard. fast fret usually makes them happy, as well as you.