Windows 7 nowadays has issues with its root trust certificate, seeing as Microsoft stopped supporting Windows 7 a long time ago. Accordingly, you may find that GameMaker will say that it cannot reach our sites (typically you would see this written in your ui.log file as a failure to log in).
This guide will give you information on how to fix this issue; however, our advice would always be to update your Windows installation whenever possible, as Windows 7 is not supported by the majority of external tools and services GameMaker relies on.
If you were to open your browser of choice and navigate to the URL which is giving you the error in your ui.log file you would then see your browser say something about .NET::ERR_CERT_AUTHORITY_INVALID (you may have cached copies of the site, so ensure you actually clear your site cache to confirm if you have the error or not).
The fix here is to first ensure your system clock is accurate and then install https://www.microsoft.com/en-us/download/details.aspx?id=45633
For more information on what that fix contains, see https://support.microsoft.com/en-us/topic/support-for-urgent-trusted-root-updates-for-windows-root-certificate-program-in-windows-a4ac4d6c-7c62-3b6e-dfd2-377982bf3ea5
Again, we cannot control for how long this fix will keep working on Windows 7 and we also strongly recommend updating to Windows 10 or 11 if you can, as many of the SDKs GameMaker relies on to do builds for different platforms already only support Windows 10 or above.
However, if you have any further issues with your system permissions stopping you from using GameMaker in any way, please see our main FAQ for the permissions GameMaker needs.