Cold water valve won't turn on to fill washer

SOURCE: Maytag washer

It sounds like you have the hot and cold water lines to the washer reversed.  Try turning off the tap for the hot water then setting the washer to just cold wash and then  hot washif you get nothing on the cold and cold water when set to hot they are probably reversed.  Typically if the auto-temp control is broken you will only get hot or cold coming out on any setting. 

SOURCE: Magtag Washing Machine Can't use cold water only cycle

Stranger things have happened.
Glad it is working for you.

SOURCE: MAH8700AWW - No Fabric Softener

Not sure if you've ever resolved this issue, but I'm dealing with it myself. I have come across this service manual that gives a very detailed illustration of the systems, how it works and how to test it.
Focus on pages 15 thru 25. Hope this helps you.
http://www.servicematters.com/maytag_library/docs/16026126.pdf

SOURCE: On our Model LAT9635AAE washing

You have a bad fill (mix) solenoid valve. The valve in the solenoid is hanging up and by switching it back and fourth between hot and cold its just working its way to the proper position..You were on the right track.....

Testimonial: "Thank you, Right on the mark! Your help is greatly appreciated! Thank you again."

SOURCE: My Maytag, Model A882 series

Good day,
This is usually caused by the dual water valve on the back of the machine failing.
It supplies both cold and hot water to the machine.
In your case, it appears the cold water side of the valve has failed.
It is a none repairable item, and you will need to replace the valve which is available at any decent sized appliance parts house.

However, before replacing the valve, make sure the cold water from the faucet is turned on, and with that hose removed, make sure cold water will come out of the hose if you turn the cold water valve on.