I'm currently running Windows 8.1 x64 (a problem in itself that I can't change sadly ;-P) with the latest version of VirtualBox (4.3.18 r96516). I managed to get the server version up and running with no issues but I cannot get the desktop version running.
I can boot to the menu and start the process (select the option to install and/or try) and it will get through the inital Ubuntu 14.10 loading screen (with the progess "bar/dots") but then we get to a nasty screen of distorted colors and that's it.
My hypothesis is that the display driver/server isn't working with VirtualBox and what I'm essentially seeing is the display in a crappy mode (16colors@62x24) because I am able to see a perfectly fine screen with cursor working and everything and then suddenly I'm in that nasty screen. The mouse does show up (nasty looking and filling the entire screen) but nothing else.
Here is a screenshot:
Here are my settings in an album (I can add more if desired but I put in what I thought were the most relevant):