I have the same problem & I own & operate a guitar & amp repair business. liamjmicallef, I am still trying to find the time to finish troubleshooting the problem (my business is growing at an alarming rate) but so far it seems to be faulty switching via the 1/4" output jack. As most of us know leaving the cable pugged in drains the battery like an acoustic guitar or effect pedal, why because when inserted the 1/4" male plug completes the circuit & switches the electronics on. To troubleshoot or see if I am correct, If you can, try a few different cables, carefully inserting them a few times each to see if you are able to turn the modeling on after plugging in (as I did). If you are able to get the modeling to come on by doing so then it's time to replace the jack assembly. Good luck finding the part number for the Variax standard jack assembly. Oddly enough the same part is available online for the Variax JTV-69, JTV-89 & the JTV-59.
Maybe if we ask nicely psarkissian will help us with any information at all, as to where the Variax Standard jack assembly part # and/or where it can be purchased?
or will he just offer the usual generic reply with instructions on how to get to that oh too familiar, cold n dark, dead end street we end up where solutions are never found?
If it's under warranty follow his instructions. If out of warranty, psarkissian, I have less than 4 hours use on my Variax standard & have babied it from day 1 - this is obviously a factory defect in my professional opinion & if a loyal line6 customer is willing to pay out of pocket to purchase a replacement part, the correct part number & where to purchase it is not asking a lot don't you agree?