The washer uses a direct drive system. What this means is that it uses a motor coupling in place of the drive belt. It sounds like to me that you have a broken motor coupling.
If the washer
will fill and drain, but won't agitate or spin, you may have a broken motor coupling. The noise of the motor engaging, lack of agitation and ability to still drain are the usual symptoms. This is a common fail item with this model washer through normal wear and tear. Newer versions of the coupler are more resilient and resist breaking. The following link explains how to replace one:http://www.fixya.com/support/r385252-replacing_motor_coupling_whirlpool_top
The motor coupling is located between the drive motor and the transmission and takes the place of a drive belt
. They do wear out and can break. The replacement part number is included in the link I provided and is an improved upgraded coupling that is more resilient. It should last longer. If you have questions, or require additional assistance, please let me know. I hope this helps you.
A replacement coupler can be purchased on line at appliancepartspros.com for about $11. Just use the part number in the link and "Search by Part Number" for your search criteria.
If you have questions, or require additional assistance, please let me know. I hope this has been helpful to you.
NOTE: Roper is manufactured by Whirpool, so the instructions I provided will apply to your washer.