Matt,
Christian may be able to give you a better answer, but based on the information in your last message I think the problem is likely with the configuration of the Windows 2008 R2 Server, your firewall, and/or the network rather than with your Win10 machine.
I think I had it backwards (I didn't read your post carefully), as I assumed that you were trying to configure your Win10 computer to accept incoming RDP connections (which Win10 Home cannot do) rather than use the RDP client in Win10 to connect to a remote
server (which Win10 Home should be able to do).
There should be no difference in your ability to connect to the Windows 2008 R2 Server using the RDP client in Win8.1 Home or the RDP client in Win10 Home (I have a Win2008 R2 server on my home network that I can connect to fine from both Win 8.1 and
Win10). However, the Windows 2008 R2 Server must be configured to accept connections from the account you are using to connect. If you have control over the configuration of the Windows 2008 R2 Server, you can add an account to the allowed Remote Desktop
Users as shown below (or alternately, you can just select "Allow connections from computers running any version of Remote Desktop (less secure)"):
Christian described how to get to this dialog in his pervious post:
"For this, please right-click on This PC, click on Properties.
From the System window that is opening, please press on the
Remote Settings link, from the left part of the page.
On the System Properties window, Remote tab."
If you do not have control over the Windows 2008 R2 Server, I would try to speak with someone who does (someone in your IT department, a System Administrator, etc.) to try to get them to make the necessary changes. Also, you may want to confirm that
your firewall is not blocking port 3389 (the default RDP port). I had some issues with this when I first set up my network. The easiest way to rule out firewall issues is to temporarily disable your firewall entirely and see if the problem goes away.
I am by no means an expert on setting up remote desktop (I'm more of a hack), but I have a fair amount of practical experience getting it working on my home network. If the above does not help, let me know soime more details of your situation and I
will attempt to help further. Thanks.
-JNP