Is the by pass valve to the heater fully open? Is the delivery valve from the heater open? Is the hot side valve of the faucet opperating?

If the pump does not activate on the hot side when the faucet is opened, it means there is trapped pressure within the line. The pump only activates when the limit switch senses a loss in pressure, such as you're experiencing when you opperate the cold side of the faucet.

I would first check the heater valves, input and out for their appropriate placements. If they are properly aligned, and there still is no water flow, turn off the pump and remove the valve assy, in the hot water side of the faucet.

Once the handle is removed with a screw on top, you can see the splined shaft that controls the valve. Remove the nut that holds it into place and lift out the shaft. The packing or valve on the bottom may have failed closed, plugging the water flow.

These parts are inexpensive, easily changed, and found at most big box, hardware and plumbing stores.