welcome. Unfortunately, Parker has ceased operations. We're all waiting on pins and needles to see what they have planned for 2017, per parkerguitars.com.
You should be able to do a quick inspection to rule out damage to the circuit board. Also, you're getting mag output after battery swap, so the circuit board is likely fine.
It would be extremely unlikely that all the piezo saddles would fail at the same time. Possibly, one failed and became noisy, so someone removed them from the circuit? Anything is possible with an old guitar.
Anyway, for the piezos, the most likely issue is with the connections from the piezos relative to the circuit board, switch, or jack.
If you can post some clear pics (need to host elsewhere and then link to it here) we might be able to see what's going on.
Backplates might be hard to find but you can try ebay, there's a guy selling stuff from the factory, wiguitar.
What shop did you visit in pgh? (I used to live there, I miss it.)