My beloved Squier Tele with DiMarzio Virtual T pickups seem to have developed a grounding problem. It hums like crazy now if I don't put my hands on the strings or on the control plate.

I took a look at the soldering, and it looks fine.

I have had some problems with my 3-way switch, and I think I'll replace it and see if this solves the problem.

Anything else I should check?