I referred to the Help menu. In this you find a function with a name like "Check for new versions" (I run the German version, so I had to translate it - I don't know if this is the exact translation).
This function tries to access the internet. If it succeeds, you get a message box, either telling you that you have the latest version or that there is a newer one. If you do not get a message box then MP3tag gets blocked by something on your PC.
In general: I think that this is an absolutely local problem. I have MP3tag on XP, W7, W8, W10 and it runs just like it should.
As I cannot look over your shoulder and check if it is the anti-virus program, the firewall, the access rights, you have to be the detective on your system.
Please check the locations mentioned in this thread
/t/964/1
if you can access them, esp. who the owner of these folders is. For this create a column in the Explorer for "Owner" and see if it is just a weird sequence of numbers and letters or something that makes sense to us humans. The latter is OK then.
But as you did clean installs, the reason for the strange behaviour is more likely to be found in conflicting programs like firewalls and anti-virus programs.