Ge washer cold water will not fill - have checked hoses, cleaned washers, checked water connections. warm and hot fill fine, but it appears the cold water is running under the machine somewhere Cold water stopped feeding completely and suddenly. Cold water going to the machine is turned on and had been working fine, and I believe all the hoses are fine because they're isolated in the space by the back wall. Now any cycle combination that takes cold water will stop and not continue when it must feed cold water. However, warm/cold will fill the washer with hot water because it's not feeding any cold, and for the spin and rinse with cold water the machine just stops, because it can't feed cold water now. (The machine was purchased 4/10/05, so it's a little over three years old.)

There is a filter screen at the washer inlets for hot and cold water. Clean the screens

The inlet valve on the cold water inlet is clogged, dirty or jammed. You need to remove the inlet valve and clean the valve and filter. use back flushing with brushing to clean the filter.
the hum you hear is of the coil working but is not opening to allow water into the system.
Also you can switch the inlet valve from the hot line if needed .
check this link for removing the inlet valve:

http://www.espares.co.uk/advice/washing-machines/a/7/1408/how-to-replace-the-inlet-valve-on-a-washer-dr.html

Turn the water supply off.
Remove the COLD water hose from the rear of the washer.
Clean the silt out of the COLD water valve on the washer.
Re-attach the hose on turn on the water supply.

The hot and cold water supply hoses that connect the washer from the water supply faucets on the wall to the water connections on the back of the clothes washer usually have filter / sediment screens within there connection fittings at the end of the hoses, these will collect dirt,sand, calcium deposits, etc.,when they trap enough of these materials they will plug up and restrict the flow of water into the clothes washer. Turn off the water faucets at the wall, and you should do this for both hot and cold hoses, disconnect the hoses from the washer and the water faucets, look into the hose ends and pull out the screens and clean them out by running water and what ever you can use to clean them completely!!!!!
Now look inside the water connections on the back of the clothes washer,where you screw the hoses on the washer, and check to see if there are filter screens in there, if there is, remove them and clean out completely also, then reverse the removal process and reconnect the hoses, makeing sure to connect the hot and cold hoses to the right connection on the back of the clothes washer!!
Try filling the washer with water to see if you have corrected the problem.
Make sure hot and cold hoses are correct on the back of the washer!!!!
GOOD LUCK !!!!!!

This is a common problem with hot water lines to washing machines. The hose connecting the washing machine to the hot water supply has a small screen in the inlet of the hose. These are used to keep grit, etc from getting into the washing machine and causing bigger problems.
Here's what to do:
Pull the washing machine away from the wall a little so you can access the shut-off's. Turn off the hot and the cold water valves.
Take the hot water hose off the valve and check the screen in the rubber washer of the inlet hose. Replacement screen/washers are available at local hardware stores for a couple bucks.
You can clean the old ones, just be careful not to damage the rubber washer because that's what keeps your hose from leaking when you reinstall it on your faucet.
While you're at it, clean the cold water screen as well.
REcheck your fill on a hot cycle... you've most likely solved your issue!

check the fill hose washer located in the washer cold water fill hose,they get clogged with lime and such,and when you replace the washer run hot water thru the hose to clean it out thoroughly,

The water fill valve - The water fill valve is a mechanical and electrical part, the coils on the valve need electricity to mechanically open the valve to allow the water to flow into the washer....myth....the washer pumps water into itself...no, it does not. The fill valve opens and the house water pressure pushes the water into the washing machine.
No cold water or no hot water - The fill valve has two coils, one for the hot water and one for the cold water. It is possible that one of the coils can fail and you loose that filling ability. If the cold water coil quits, the hot will still work and during warm fill you will get hot water only and during a cold fill you will get no water at all. If the hot coils quits, you will still have cold water fill, cold water only on a warm setting and no water on a hot fill setting. You can No cold water or no hot water - The fill valve has two coils, one for the hot water and one for the cold water. It is possible that one of the coils can fail and you loose that filling ability. If the cold water coil quits, the hot will still work and during warm fill you will get hot water only and during a cold fill you will get no water at all. If the hot coils quits, you will still have cold water fill, cold water only on a warm setting and no water on a hot fill setting. You can test a fill valve live for 120 volts, power to a fill valve coil and no fill = a bad fill valve. You can also test the coils for continuity, no continuity = a bad fill valve. Some Maytag washers have a fuse in the fill valve circuit, if this fuse let go the washer will not fill. Fill valves can also from time to time stick open and not stop filling. If you have to shut off the fill valves to stop the water from filling in the washer, you have a bad fill valve and you will have to replace it.

If you hear a humming, the coil on the water valve is probably OK. On warm, you are getting cold fill only. (hot + cold = warm) Take the hot water supply hose off the machine and look inside where the hose attached to the washer. There should be a screen inside. Remove it and clean it out. Also, check both ends of the supply hose, as sometimes you will find a screened washer in there too.

replace the water inlet valve

if you are only getting hot water on warm setting possible bad inlet valve cold side ck wiring first just to be sure wire to cold side not loose