I've seen this problem numerous times and was just able to replicate it this morning.

I was working to fix a offline files sync issue on this machine and configure DirectAccess on this desktop. Once I got the policy applying on the machine I tested DirectAccess and it was working properly by using my cell phones hotspot. Once I was satisfied it was working properly I disconnected from wireless and connected the machine back up to the Intranet via ethernet. After a few moments I had a network connection again. IPConfig reported that the machine was able to get an IP address via DHCP. The DCA agent however was red and reporting problems. I then noticed that under the adapter settings for the NIC it was stuck at "Identifying Network". When I ran wf.msc I could see the public profile was active. I could connect to the majority of Intranet resources I tested including our NLS site. I was however unable to kick off the offline files sync process (I suspect it will not start if it's using the public firewall profile). I was unable to change the profile in use to domain. The only way I could get the machine out of this state was to reboot the machine.

 I tried to install this hotfix but it's already present on the system.

https://support.microsoft.com/en-us/kb/2680464