I found out what the problem was; turns out it was a ATI Rodeon Graphics Card Driver issue:
Ubuntu 10.04 tried to emulate the ATI Rodeon Driver for my card and they did it pretty well, and I thought it was the proprietary driver since the Gnome Window Manager spat out a message that says: “Proprietary Drivers Are Available,” and I thought, “Oh great, now I don’t have to go through all the trouble of going to the ATI website, downloading the driver, and installing it by hand.”
Well, just so you know, “Proprietary” in the ubuntu manager isn’t the same as the real deal, folks. No…You still have to go to the ATI website, get it from source, and install the ACTUAL DRIVER by hand. When I did that, fixed the problem. Blender worked like a charm.