I did a "Reset" on IE from one of the other replies above, but no luck. My primary browser is Chrome, however. Still unable to connect to ArcGIS Online from ArcMap (either browser works fine.) When I hit "Trouble Connecting?" It fails all of the tests (proxy server, download speed, network latency, and network route).
I've tried other solutions such as deleting registry for AGOL, and also adding AGOL domains to Internet Explorer's trusted sites. None of this was a reliable solution as they only worked at times.
I've tried connecting to AGOL via https and this has been consistently working for me.