My GE washing machine (top loading Deep Fill) sporadically beeps and its lights flash when the machine isn't in use. I'm concerned about a potential electrical fire.

SOURCE: GE Profile WPRE6100G Top Load Washer

The most likely cause of your problem is the lid switch.

SOURCE: GE washer won't fill with cold water

Cold water pipe had become frozen. FYI this model of washer has a nice feature whereas you can test each component i.e. valves, by setting the timer and reading the LED's on the front panel. Instructions are in the schematic.

SOURCE: Appears to have turned on but won't start running water to start

There's an error code on the digital display

It doesn't work at all
It won't drain
It doesn't spin
It doesn't agitate
It's noisy
It leaks
It's off balance
There's no hot water
There's no cold water
It's slow to fill
There's no water at all
The clothes are wet after spinning
The cycle doesn't advance
There's no delicate or regular spin or agitate
It's overfilling
It's underfilling
The water temperature is incorrect
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SOURCE: Fisher & Paykel GW612 Top Loading Washing

Hi there
That fault is the pump blocked error (no change in water level).
i have a quick and easy way to solve this problem.

first turn the machine off then tilt the machine back and lean it on something(a chair or wall), look underneath, in the top right hand corner of the plastic outer boul you will see a small pump motor it has a fan on it spin this fan and if it is hard to turn that means there is somthing stuck in the drain pump keep turning the fan and try to free whatever is stuck in the pump, then try the machine on spin again all goin well the object in the pump should come out with the drain water(doing this will not harm the machine) if the object is still stuck you will need to get the water out of the machine (bailing or siphioning will work) and tilt the machine back again and take the wires off the pump and there should be a white tab on the boul holding the pump on pull this tab and twist the pump anticlockwise about a quarter turn(you will need a few towels or a boul or bucket to catch the water) and it should come off exposing the blockage.
Hope this solves your Problem.

Nick

SOURCE: ge washer

Pull up sharply on the agitator to remove it from the shaft. Check the agitator mounting cup underneath it is probably stripped out. It is a replaceable part.
If the agitator is difficult to pull up,use a old strong leather belt under the agitator and pull it off using the belt.