Will not agitate motor runs whirlpool lsq9610jq0

It sounds like you may have a broken motor coupling. This is the most common cause of the symptoms you are describing. Whirlpool manufactured top loaders use a motor coupling in place of a drive belt and are known as "direct-drive" systems. No agitation, or spinning, associated with a grinding noise are the usual symptoms. The washer should still have the ability to drain, however.

The following link explains how to access the coupler and replace it, if necessary:

http://www.fixya.com/support/r3574231-replacing_a_motor_coupling

The part number is included with the instructions I provided. Replacement parts (if required) can be purchased at any of the following websites:

searspartsdirect.com
pcappliancerepair.com
appliancepartspros.com
repairclinic.com

All these sites are reputable and offer great service with competitive pricing, so shop and compare. The first three sites I listed also include helpful exploded view parts diagrams to assist you in locating and properly identifying the parts you need. If you do not wish to order parts on line, use the part numbers I provided and go to your nearest appliance parts retailer. The coupler is usually sold as part of their in-store inventory. The average cost of a motor coupling is only about $15.

Another cause would be a failed gearcase (transmission). I would recommend checking the motor coupling first, however. If the coupler is still intact, please let me know. I can give you guidance on how to replace the gearcase, if necessary.

If you have any questions, or if the symptoms I describe do not match the problem you are experiencing, please post back and let me know. I hope this helps you.