First, you must be running an X server on your PC (Exceed, Reflections, XWin32) See
www.xwin32.com for a trial version of their product.
Second, make sure you have X forwarding enabled in Absolute. Check Options->Properties->Connection->SSH2->Forwarding. If it is not enabled, enable it and disconnect/reconnect to activate it in the current session.
Third, check your DISPLAY variable. It should look something like this:
localhost:10.0
The SSH server will set this value for you at login time. Any attempt to change it will result in failure. Check you profile and startup scripts to be sure that you're not setting this manually somewhere. ':0.0' is wrong and refers to the X display on the server, not the client.
If the DISPLAY is either not set or set improperly, then it's possible your host does not allow X forwarding or you are overriding it somewhere.
Hope this helps.