I had this same problem on my gs3 a few months ago. It is a hardware problem, not caused by your rom.
What I did, is I found a guide (use Google, I can't remember where it was) that walked me through flashing everything back to stock. I then took it to the store, and they hooked me up with a replacement.
The guy at the counter had never seen it before, but it was clear that it was a hardware malfunction, and therefore not my fault.
Maybe you can do the same
I would do this as well but I don't think I can flash the unsecure bootloader on the replacement.
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