#3
could it be that the volume on the guitar is stuck at zero? I've noticed when you get a guitar and turn the volume pot right down then play it, you can sometimes still get a very faint sound.
#4
dry solder joint. happened to my LP when i rewired it.
GEAR:
Epiphone LP special model 2 (Heavily modded - killswitch and custom midi X-Y touch pad).
Digitech Whammy, Zvex Fuzz Factory, Boss Dynamic Wah, Electro harmonix Little Big Muff, Zoom G7.1ut, Digitech Grunge, Korg KP2.
Marshall AVT 50x