The power module is required for the VDB770. The voltage reading is definitely the problem and means that something along the circuit is at fault. That may be the power module or the wiring somewhere along the length.
How long was the doorbell working normally? Have you had storms or any work done near the wiring?
It would be good to try disconnecting, stripping back fresh wire, and redoing the connections along the circuit at the doorbell and transformer. If there is no positive impact to that voltage reading I would replace the power module.