Paul,

Sounds like a bad fill valve (cold water solenoid) or maybe the hose and valve screens are clogged with debris or sediment, it could be the water faucet is off,as well ?

Or at least, that's were I'd start,

You wouldn't notice that in the wash cycle fill, the rinse cycles are automatically Cold fill in most washers nowadays.

A proper model number would have been more beneficial, but not to worry,
I'm pretty sure you'll find the problem in the above mentioned checks.

:) :) :)