Rinse cycle, water won't work

It sounds like you either use warm or hot water for the wash cycle. If this is the case, you probably have a cold water solenoid problem on your water inlet valve (also known as a mixing valve on some washers). Most people use warm or hot water on the wash cycle. The water inlet valve has two solenoids. One for hot and one for cold. It uses a combination of the hot and cold solenoids to make warm water. The rinse cycle on most washers is a cold water rinse only, however. This would explain why the water appears to flow normally when it fills during the wash, and only trickles when it rinses. If you live in an area that has hard water, or if you use well water, these valves commonly clog with sediment. You can shut off the water, remove the hoses, and attempt to clean the sediment screens to see if the water flow improves. If it doesn't, you will need to replace the valve. The following link epxlains how:

http://www.fixya.com/support/r600647-replacing_water_inlet_valve_kenmore

I know the link says this is for a Kenmore or Whirlpool, but also applies to a Roper. A replacement valve can be ordered on line at searspartsdirect.com. Just type in the model number and the part you need is located under the "Controls and Rear Panel" heading as item number 18 (part #285805). This is a very simple and inexpensive fix if you wish to perform the repairs youself. Not to mention, you can potentially will save hundreds by avoiding the labor charges of a service call. I hope this helps you. If you require additional assistance, please let me know. Hopefully, a good cleaning will do and you won't require parts.