The sign in page is trying to connect to arcgis.com, yes you are correct, it sounds like you either don't have internet connection or the application (AppStudio Desktop) cannot access arcgis.com (firewall related issue).
Can you try opening the AppStudio Desktop using different user or Administrator?
We are able to run it with admin credentials. I also have full permissions for all GIS related file folders. Could there possibly be something Appstudio is using which I do not have access to that is not an ArcGIS product?
I have personally never seen this exact behaviour, normally it is a network connection or internet related issue. since the sign in page is just trying to open an OAuth2 login page from ArcGIS.com.
It could be an installation issue, and/or permission issue. Which user did you use to install the AppStudio Desktop with? Re-installing with the correct user and permission could help.