Sounds like it's only making partial connection. Electrical contact spray is relatively cheap and will not harm anything. I agree with Ids that it's not the input jack. It's either the switch itself, or the wiring of the bridge pickup. Most likely the switch.
Contact cleaner can be sprayed into the switch from the front (spray a bit - not sparse, but don't soak it either) and then work the switch back and forth a few dozen times - like a child sitting in the passenger seat of the car that can't leave the power locks button alone. Wipe any contact spray off the body of the guitar.
If that offers no improvement, take the cover off the electronics cavity on the back of the guitar. That's the weird, not-quite-circular cover back there. Once inside, you can use the contact cleaner on any connection or joint, but focus on the three-way switch's connections.
If none of that helps, bring it back to the store. They can either fix it under warranty (if you bought it new) or *should* fix it free or cheap if you bought it from them used.
Contact spray will NOT void any warranty, and the only possible damage it could do is if you left it on the paint.
