Hi Christopher,
Thanks for posting in the community. We are happy to help you.
Per your description, I would like to know which bit version of Microsoft SharePoint Designer 2010 you have installed. I suggest you install another bit version of Microsoft SharePoint Designer 2010 and then check again. Also, the 32-bit edition is suggested for most users.
Microsoft SharePoint Designer 2010 (64-bit)
Microsoft SharePoint Designer 2010 (32-bit)
Additionally, I suggest you check the system requirements mentioned in the above pages or the following screenshot.

If the issue still occurs, since SharePoint Designer 2010 only connects to SharePoint 2010, and our team focuses on queries about SharePoint Online in this category, you can post a new thread in the Microsoft Q&A Community (assign the tag SharePoint Server)for expert help.
Appreciate your understanding and patience.
Sincerely,
George | Microsoft Community Moderator