FW (FireWire) DI (Digital Interface). If the guitars don't hum with your analog gear, the wiring must be good. Digital gear is no more or less susceptible to (EMI?) hum than analog gear. The front and back ends of a DI are analog preamps like in a guitar amp or pedal. Unless there is something wrong with the internal connections in a properly constructed DI, I don't think it's possible for hum to occur internally. It's possible that the DI PSU's are creating hum in the guitars, or in the cabling. Maybe the PSU's are near an internal wall junction box? Not sure what else to suggest. Good luck.

Add: if any guitar shielding is somehow connected to positive, it could be picking up PSU hum? Does it get louder if you put the guitar closer to the PSU? I'd say the leads are switched at the jack, but you said the hum goes away when you touch the jack plates.

Edited 1 time by gckelloch Oct 29 13 6:27 PM.