You don't mention what kind of graphics card in your laptop. Intel chipsets and
Nvidia are quite well supported and ATI is coming onside and new drivers should
be available soon. When you run the Live Cd you can change the boot parameters,
including graphics resolution. You should be able to boot into one of these, as
even low res is supported. Look to the bottom of the grub boot screen. Press F4.
Change the resolution and see if it helps.

Also try this: At the bottom you can see a box beginning with the words boot
options with text written in it afterwards. It will change as you cursor through
the menu. Look at the end of the line and remove the word quiet. This will allow
you to watch the boot process and see if it stalls and what is causing the
problem.

See: https://help.ubuntu.com/community/BootParameters

As to why 6.10 worked and 8.04 didn't, has to do with the amount of data that
will fit on a disk. Support for older hardware gives way to support for the
newer, in the same way that Windows 95 drivers won't work in XP or XP drivers in
Vista. The drivers are specific to the kernel. Ubuntu 6.10 would not upgrade
because it is past its support period. It expired last April. See:
https://wiki.ubuntu.com/Releases

Good luck. Let us know how you do and please provide as much info as you can
when requesting help. In this case you need to tell us the graphics card since
it is a graphics problem that you mention.