I have been unable to connect to the remote server from my ArcGIS desktop for some time now. Everything from Add Basemap to Add Data from ArcGIS Online. I am currently in 10.2 with the most current service packs.
This has actually been going on for a couple of years since at least 10.0
I had hoped when we upgraded the issue would go away.
I do have a valid ArcGIS Online log in.
I can log in from and MXD and upload data to my clients ArcGIS Online account, and I can log in via a web browser to AGO
However, if I click on Add Data and try Add Basemap or from Online, or I click File>ArcGIS Online I get the Unable to connect to remote server message.
Is the sign in to ArcGIS Online button even available? It's possible something is getting blocked. If you can use a program like Fiddler, which logs network traffic, you may be able to see some error messages.