Thank you for your question.
I can understand that having your carpet cleaner not working when you want to do some cleaning would be a concern.
I can see that you have done a good job of diagnosing the problem. The solenoid not having any continuity certainly can be the issue.
I am going to include a troubleshooting guide to help you diagnosis your problem further to make sure we have covered all the possibilities.
Before you order the part, look on the bottom/back of the machine for the complete model number, so you will be ordering parts for the correct model.
The Part number I have found for the valve solenoid is: 2036761 and you can order that from
Sears Parts Direct
I hope this will help.
Thank you for using Manage My Life.