I've installed several ArcMap servers and until this latest install have had no issue publishing web services from ArcMap to ArcGIS for Server. I have a Windows Server 2012 R2 Standard with SQL Server 2014 and ArcGIS Server 10.4 installed. From ArcMap 10.4 I am able to connect to the database and view data in a point feature class. When I choose "File->Share As Service..." and choose "Publish a service" from the first dialog, I then choose my server connection and give the service a name. On the third dialog, I'm able to choose the "Use existing folder" option and choose the folder that I created using Server Manager. When I click "Continue" from this dialog, the dialog never returns and I eventually have to end the task using Task Manager.
I'm not seeing any helpful error logs on the server and have not had any issues publishing services until now. I've install ArcMap desktop 10.4 on the server and I get the same response when trying to share the feature class as a web service.