At the washer, I disconnect both hot and cold lines feeding washer. There is no hot water coming out of wall at washer. Rest of house is fine. I have a 13 yr old gas water heater in Phoenix, it is summer now. Could water heater be showing first signs it is about to fail? Again, rest of house hot and cold water is fine. Wash room is 5-10 ft from garage based water heater.

What you describe indicate a problem with the hot water valve at the washer or that there is a stop valve on that line that is closed. Not symptom of water heater failing.

Turn the water off at the water heater and op[en up the valve, Check for trash and turn the hot water on for a second to be sure you're getting pressure to the valve. If you get pressure check the washer's secured and reassemble, Better now? Good luck. Tom