I have seen this problem before and it usually turns out to be a timer issue. You see, the timer on the GSD models sends voltage to the water valve only for a brief 2-minute time at the beginning of every wash and rinse program. If you manually advance the timer, it may skip the fill, as the contacts are somewhat delicate and difficult to initiate this way. When I test one of these models, I turn the timer ever so slightly until it barely comes on, then wait with my meter until the fill signal starts up about a minute later. If you try to advance it to fill, it may miss out. When it starts skipping the fill occasionally, replace the timer.
Wiring issues can occur, but are rare on this model. The timer on this model can be easily damaged by attempting to turn it counterclockwise instead of clockwise to set. Usually, timer failure occurs on this model due to little hands meddling with Mommies dishwasher, but it can occur with no help at all just from years of use. The GSD is a very old machine.