Hello,
Sorry to hear you are having issues. First check in your account and see if ObjectDock listed there. https://store.stardock.com/myaccount/products. If not listed there. You might purchased ObjectDock under ObjectDesktop package which is subscription package.

But I believe you still can manage your old activation by using this guide : https://forums.stardock.com/486311/accounts-and-activation-support-faq#deactivateproduct . Do let us know if you still need our assistance.

Thanks
Basj,
Stardock Community Assistant.

No, the refund was for ModernMix which I had already purchased for a Sony laptop with Windows 8.1.  When I purchased Start8, it also said I purchased both Start8/Modernmix combination and charged me for it again.

Hello,
Sorry to hear you are having issues. But, you should not have posted your product keys on public forum for everyone to use them. Please raise a new support ticket using below link and includes all your details there and support will help you from there.

https://stardock.atlassian.net/servicedesk/customer/portal/4

Thanks
Basj,
Stardock Community Assistant.

You can select under Account Management or Purchases and then select Ask a question. And from there you can mention what your problem there and upload your supporting files there ie payment receipt etc. 

Press "Account Management"-> "Ask a Question" should bring you to something like below:

Also, do note that, you do not need to login there to submit a support ticket.

Thank you,

Basj,
Stardock Community Assistant