You do not need a GUI - VNC will map your console without issue. VNC does do a graphic interface but if you do not have a GUI it will just treat VNC as if its a monitor out, which is different than serial but provides a very similar end user experience and will also provide access to your server.
If you just get a large black box click on it and hit any key that's just a screen saver.
Sorry to hear you had an issue with support we usually just recommend customers try Chrome if they havent and that works for most of them.
It seems that Firefox indeed doesn't work (Firefox 19.0 / Fedora Core 18.) If this is unfixable (which I hope it isn't, since it'd be nice to be able to use the browser I'm always using anyway for console access also) could you at least add a note to the console page about this? I didn't realise that the console was supposed to open in the browser window and thought that it's broken altogether.
I tried to access my droplet via browser, I tried by Chrome, Chromium, FF and neither worked. I'm using Ubuntu 12.04 LTS in my own machine and I tried access by RealVNC and didn't works (I installed VNC server in my dropled...) as well.
There is any suggestions to access my droplet via graphical interface?