Very confusing water issue - not flowing to some faucets after de-winterizing

I think these systems are pretty basic with the only check valve being in the water heater. That check valve can come apart and pieces will flow downstream until the first 90  degree bend. But you have no cold water flow so that's probably not it.


When you turn on the kitchen faucet does it  sputter and does the water pump run continuously like the water is flowing somewhere?
Maybe try disconnecting the tubing at the water pump and at toilet and use your compressor to blow air backwards toward the pump.