There is no cold water relay. There is a water inlet valve with a cold water solenoid on it, though. If you have no cold water, any of the following could be a cause:
1. Clogged sediment screen on the cold water inlet. You will need to shut off the water and remove the fill hose from the back of the washer and check the inlet screen on the cold water inlet on the back of the washer. Clean if necesssary. NOTE: This can be a common problem if you have hard water or use well water. Cleaning with a 50/50 solution of distilled vinegar and water using cotton swabs can dissolve most accumulations of rust and sediment.
2. Poor electrical connection on the cold water solenoid on the inlet valve. Locate the electrical connection for the cold water solenoid (usually color coded BLUE for cold water, RED for hot water) and unplug. Check the electrical contacts for any signs of corrosion. Clean the contacts if necessary.
3. Bad cold water solenoid. With the electrical connection removed and the washer unplugged, take a resistance reading on the solenoid contacts. They should read something around 600-800 ohms if good. If bad, you will need to replace the water inlet valve.
4. Kinked or clogged fill hose.
NOTE: Make sure you UNPLUG the washer before servicing.
If you determine the water inlet valve to be defective, the following link explains how to access and/or replace:
The part number for the inlet valve is 285805 and can be purchased at any of the following websites:
Prices will vary between these sites, so shop all of them for the best price.
If you need a diagram to assist you, the first three websites mentioned usually have excellent exploded view illustrations that accompany their parts lists. You can use these as a helpful reference. The water inlet valve is listed as item 18 under the "Control and Rear Panel Parts" heading.
If you have any questions, please let me know. I hope this helps you.
NOTE: Roper is manufactured by Whirlpool, and use Whirlpool parts, so these instructions will apply.