The problem you encountered once you booted into Natty either LiveCD or an actual installation is that (nasty descriptive adjective) "Nouveau" driver. The open source version of the Nvidia driver. Unity requires a video driver capable of 3D acceleration which the nouveau driver does not have out of the box. It has to be enabled via the "Additional drivers" applet and even then it's experimental. Might as well install the real Nvidia driver while you're in the applet which works like a charm. The ironic thing is the Intel 45/43 GMA driver which is capable of 3D acceleration by default is built right into the Linux kernel that comes with Ubuntu (and even most other distros with older kernels) so the on board video of the majority of desktop PC motherboards will run Unity without a problem. Those with laptops are another story though. Canonical dropped the ball on this one especially for those with Nvidia video cards. Not too sure about ATI though.
On a side note, if Ubuntu actually became pre-installed on the more popular PCs (desktop and mobile) as Windows does, users would never encounter these problems. But then reality sets in.