I'm sorry to hear about your issues. I had/have the same issue . . . AGAIN WITH MY Variax. Battery charged, authentic battery, and also new authentic battery. Plug it in, green lights. Play a little, slam the guitar select switch to get it to actually engage, play a strat in position 4, then guitar goes silent except on the mags, which still work. Re--charge the battery. nothing. Leave bateery in overnight, green lights, it works, for a little bit. Same problem. Nothing except mag pickups.
Leave it in again, now it works.
Line6 - how about letting us know what the issue is.