UPDATE: Potential fix (?)
I realized that I was opening D2R from a desktop shortcut that bypassed the Battle.net Launcher app. Each time I used this shortcut, I experienced the same result described in this initial post. Upon using the Battle.net Launcher app to open D2R, I was able to connect to the online characters screen. This seems like a bug. Either the shortcut should always open the Battle.net Launcher or, if it bypasses the Launcher, should allow the user to connect.
As several others have posted in the support and bug report forums, I am unable to connect to the server after waiting in the queue. This has been occurring all day today for me. The user flow is as the title describes: I am placed into the battle.net server queue from the main title screen automatically. Then it loads the Offline characters screen (without a response window from the title screen queue). Then, when I click the Online tab in game, I am placed into the queue again (sometimes there is no queue at this point and it attempts to connect immediately). Invariably, I receive a Cannot Connect to Server response window at this point.