Remote Desktop Connection can't connect to Windows Server 2012

I have noticed that sometime enabling remote desktop does not correctly enable the firewall exception for port 3389. Please check whether the appropriate rule is enabled. If it is, try disabling and immediately enabling the firewall. This worked for me on several occasions.

You'll probably need a CAL (Client Access License) in order to access the Windows Server 2012's resources.

I was in a similar situation to you OP. I had a group policy to enable RDP. I checked that this was applying, and that I could ping the target server. In the 2012 server manager, it said "Remote Desktop: Enabled".

However, after following the steps posted by sushant (cmd > systempropertiesremote) (which can also be reached by other methods e.g. sysdm.cpl) I reached the "Remote" tab of System Properties and saw that "Don't allow remote connections to this computer" radio button was selected. This was clearly the cause of my issue and as expected, selecting "Allow remote connections to this computer" enabled me to mstsc into the server.

I also had another instance where even though RDC was enabled, the firewall port wasn't opened. I now have as standard in any domain I manage two policies, one to enable RDP, and the other to allow it through the firewall.