Blue icon with a question mark - what does it mean?

This SQL server icon ( blue question mark), indicates that white question mark on blue circle icon means Status Unknown, SSMS does not know if the service is running or not, by way of a WMI call. I'm quite certain this icon replaced the blank or white circle icon of prior SSMS versions.

After some digging, it looks like you could run into one or more issues causing this behavior, as follows:

• See if TCP port 135 to the server is open or not on your firewall? If it's not, opening it up may resolve this icon, but understand that there are also some special considerations to be aware of when enabling this port. Normally, this isn't a big deal if the server is not exposed to the perimeter of your network, but if your firewall rules are very restrictive or this server sits in a DMZ, this may be something you have to live with.
  
• Your user may not have proper permissions to view the service state remotely. To enable those permissions, follow the instructions here.
  
• WMI services are not running on the server hosting the database engine. Start the WMI services via services.msc, etc.