#1
I have active pickups. EMGs specifically. One pickup suddenly started producing all kids of static noise. If I switch pickups it is silent
#2
try changing the 9v battery first. if that doesn't work check all the wire connections
2002 PRS CE22
2013 G&L ASAT Deluxe
2009 Epiphone G-400 (SH-4)
Marshall JCM2000 DSL100
Krank 1980 Jr 20watt
Krank Rev 4x12 (eminence V12)
GFS Greenie/Digitech Bad Monkey
Morley Bad Horsie 2
MXR Smart Gate
#3
Probably not the pickup itself but the selector switch, or perhaps a loose wire as Robb said. Battery change isn't a bad idea while you're at it but this sounds like a bad switch to me.