#1
So I recently bought a Parker PDF 100 (ngd incoming!) And the bridge pickup isn't working. I'm getting no sound from it, except it works if I have the coil tapping active. When I have the selector switch in the middle position, I can only here the neck pickup.

Is this a wiring problem? I don't know a ton about guitar wiring.

Thanks in advance
The gear:

Carvin Bolt Classic
PRS SE Singlecut
Agile AL-1900
Peavey Vypyr 2
#2
It sure sounds like a wiring issue. Take it back to the store you bought it from and make them fix it for free for selling you a product with an issue.
#3
If it's working in split coil mode then it sounds to me like it's a 4 cable wiring (with additional bare wire). The cable that's meant to go to the ground is not connected so the pickup has two ways for the signal to go, one of which is going nowhere. But when you split it, a ground connection is made and you hear sound. Check for an unattached wire.
"Air created the greenness. And once you've got something, that leads to otherness." - Karl Pilkington.