I have a GE GSM603X-68AW dishwasher. A few weeks ago, it suddenly stopped working. When I lock the latch, I hear a buzzing sound. When I turn the timer knob timer to "Start," nothing happens. If I advance the knob timer to "Short Wash," "Rinse & Holds," and "Plate Warmer," I hear a clunking noise sporadically as I turn the knob. Occasionally when advancing the knob timer slowly, some water will flow into the dishwasher at some point in the cycle, then stop, and then nothing happens.

Since this doesn't really fit any of the troubleshooting scenarios that I've read about, I'm not sure where to start. I was going to remove the water inlet valve to check if there's any blockage (it seems to have continuity), but I'm having difficulty separating the valve from the copper supply line. I was able to loosen the nut, but the supply line seems like it's fused to the valve. I've wrapped a paper towel soaked in vinegar around the connection three times, and it still won't budge. Am I missing something?

Any other suggestions on how to troubleshoot this problem would be appreciated.

It only fills with about an inch of water, and that's even rare. If I just set the timer to "Start" and let it run on its own, nothing happens. The one inch of water only occasionally fills if I manually advance the timer knob.