I have a Compaq 6820s, which is a Intel dual-core laptop with an ATI Radeon Mobile X1300 and 2GB of ram.
I was running 10.2 x86 without too many problems.
I installed a new hard drive and loaded up 11.1 x86-64 on it.
For the most part, it runs well, as long as I am on AC power.
If I try to boot on battery, however, it never gets to the greeter, locking up on a black screen shortly after selecting the OS from grub. (the screen is ON, as the backlight is active, just no image)
And 50% of the time the system will lock up hard with a distorted display if I disconnect the AC power while running.