what would make my kenmore washer not use cold water all of the sudden?

Assuming no one has turned off the cold water tap, the problem is most likely the water inlet/fill valve.
Its the piece your hot and cold water hoses fit on to.
This piece has 2 valves in it to allow hot or cold or both (warm)
water in.
Hot setting: hot side opens.
Cold setting: cold water side opens.
Warm setting: both sides open.

Fairly inexpensive part just call Sears and have your model #
handy (its located on the machine in the door cavity on a mettalic tap. Probably starts with 110 or 970 )

Chris
December 2005