It is possible that the graphics card on your new computer is not fully supported with the drivers available for 10.04.
As an experiment, load 12.04 (Beta) onto a Live USB or Live CD and run it. Open a terminal (press Ctrl-Alt-T) and enter the following two commands:
The first command will display "ubuntu" if the graphics card is full supported, and "ubuntu-2d" if not. The second command will display "Yes" and not "No" on all lines if fully supported.