Could not find an active case record type named 'Product Support' for the 'Product Support' support process.

Hi , 

I thought I had the same problem with Billing,  It was only when I went back to "Support Processes" under the quick find,  I had not added Billing.  So I added it,  and then had to go to the object case and record type and adjust the Billing in there from Product support to billing. 

I had the same issue, you probably forgot to complete bullet point number 7 under "Create a Support Process", if you don't create the support process for "billing" it won't show up in the drop-off list. It's an easy fix.

Go back and add the support process, then you can go back to the record type, click edit and then select billing.