Hi. If you have not done so yet I would disconnect the cold water hose at the back of the machine and check to make sure the hose, and screens are clean.
If you have a multimeter check for 110 vac at the cold water valve wire connectors inside the machine. If you unplug the washer, disconnect the cold valve wire connectors and set the multimeter to ohms then you should probably read something on the order of 900 ohms on the water valve coil. If it reads very high ohms then the coil is bad, and you should replace valve. Also, check for corrosion on the terminals as that can be an issue with it not working right.
If you have 110 vac at the water valve, the ohm reading is good, but the screen in the the valve looks bad then I would probably just replace the valve. | 
Washer (cloths) 
