Water only heats when pump is on

If I turn on my barista machine, the ready light never turns on. I originally thought the heating coil may have gone bad.

However, I tried descaling the machine, and during the descaling process, I noticed that the water does heat as long as water is flowing through the machine. After I finished descaling the machine, I tried to use it. Same problem - the ready light never turns on and the water doesn't heat. If I turn the pump on, the water coming out of the machine will heat to ~165°F after about 30 seconds.

I think it might be a sensor issue, but I don't want to start buying parts unless I know for sure what the problem is.

Does anyone know how to fix this problem?