So to review:
1. There's water in the water heater tank.
2. There's water in the fresh tank
3. If the water heater bypass is OPEN, and a HOT faucet is opened, water comes out the faucet.
4. If the water heater bypass is CLOSED, and a HOT faucet is opened, no water comes out the faucet.
5. If the water heater bypass is CLOSED, and a COLD faucet is opened, water comes out the faucet.
6. The antifreeze suction line valve is closed.
7. When the pump is on and the water heater pressure relief valve is open on the outside, water comes out.
The fact that water comes out the cold faucets but not the hot suggests that water is not getting out of the water heater. If everything you've reported is accurate, I'd guess there's a problem with the valve on the water heater outlet, or if there's a check valve, as Dave suggested, a problem with that check valve.