Remote Desktop no connection

Hi,

I have a late 2012 Mac mini server running Mavericks 10.9.5 Server, recently refurbished by Apple. I have been unable to connect to it with Apple Remote Desktop or any other vnc viewer including OS X's built-in screen sharing. Remote management & screen sharing are enabled in both system preferences - Sharing, and the Server program. The target computer shows as "available" in ARD, but connections always fail and I get the message that I should make sure that these things are enabled in system preferences, which of course they are. The only way I've been able to get in remotely is with Team Viewer, but I prefer to use ARD which I use with a number of other Macs

In desperation I installed a copy of Vine vnc server and in its configuration dialogs I saw something interesting. It said that the System vnc server was not running(!) Activating it manually from Vine did enable me to connect from my MBP using ARD, but only like a common vnc viewer (ie, no data encryption).

Also, strangely enough I have these other unusual symptoms: 1) before using Vine to start the system vnc server, even though I couldn't make a remote desktop session successfully, I was able to sleep and wake the remote Mac mini from the Manage menu in ARD. 2) Every time the Mac mini boots up I am prompted to approve income connections to ARDAgent.app even though it is pre-approved in the Firewall advanced settings. BTW, turning the firewall off has no effect on connections - they still fail.

Any ideas? All guidance much appreciated.