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Replacement parts for GE GSD3230ZZ2WW | AppliancePartsPros.com

Check that the float is activating the overfill switch. It may be stuck in the up position or for some other reason not activating the switch Item 307 in "Body parts" section

If you do not have a meter, you may want to get one.

Check that the overfill switch's contacts are actually closed.

You can then check the valve coil for continuity, if open it is shot.
Can also check that it is getting 120 volts to activate it when the unit should be filling.

One other thing is that the water valve has a screen filter on it's input side.
It may be clogged up.
Shut off the water supply.
Check it, if clogged up clean it. Do not remove it from the valve, it is there to prevent crud from getting into the valve, holding it open and causing a flood.
Have a shallow pan and towel handy to catch the water from the line.

I would suggest you purchase a meter. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.