To check the IPv6, which the troubleshooter should have done, use
ncpa.cpl to open the network adapters panel. Select your adapter and right click - properties. The IPv6 entry should be checked.
From the Microsoft Store:
You can join a homegroup in any edition of Windows 7, but you can only create one in Windows 7 Home Premium, Professional, Ultimate, or Enterprise editions.
I will assume you are on the same local network for your system. If you are not sure, open a command prompt and type :
ipconfig /all > %userprofile%\Desktop\Ipconfig.txt
You can copy this and then paste into the command window by right clicking the window.
Then copy and paste here or attach using the paperclip, if you want. If it shows something you don't want seen, edit before you attach it. The local IP address should be about the same for both systems, except for the last set of numbers.
Can you see the other computer on your network in Explorer?