Not sure whether I can boot up my external usb harddisk on both from the notebook and desktop.

I installed fedora 9 on the usb harddisk by using notebook, so it detected the video card based on my notebook ( Mobile Intel 965 Express Chipset). Every work fine and able start x windows.

subsequently I boot the usb harddisk from the desktop, it boot all the way till the login prompt and stop there, it not able to continous from here even I run startx, suspect it unable to detect the graphic card (ATI Radeon HD 2600XT).

What can I do to make it work from both the system? hope for help. thanks

I don't think you're going to be able to get it working just right like you are trying to do it. I think you should partition the drive and put a version for the notebook in one partition and a version for the other computer in the other.
But, for your immediate problem, you can either run X configuration utility each time you switch machines, or you can set the driver for video to "vesa", which will be slow, but will work on most video cards. your X configuration file is probably in /etc/X11/xorg.conf