City Water is NOT routed THRU the on-board pump.
They BOTH supply the SAME cold water plumbing lines
City water inlet goes to cold water supply....pump discharge goes to same line
Pump has an INTERNAL check valve (single diaphragm) that stops city water from back-flowing thru pump
City water inlet has a check valve that stops pump discharge from flowing out city water inlet
IF city water check valve fails..water drips out onto ground
If pump check valve fails...water flows back thru pump filling fresh water tank
Pump check valves are available and requires disassembly of pump
As for pump not turning on...
*W/O city water pump pressure switch turns pump On/Off....pressure switch can be replaced
**Multi-switch for pumps use a 'latching controller' which could be faulty
7A or 10A controller used