I have similar difficulties, and have found no solution yet. I even hear the Ubuntu tone as if the machine has reached a logon screen, but all I see is the blinking cursor.
It appears that the 12.04 LTS livecd doesn't do well with some graphics cards or certain chipsets, because it relies upon a preset environment (I have a recent nVidia card). I've been digging and found that in some cases, there have been two solutions that have worked, though neither has for me. Here's the instruction, apparently issued once the system has booted:
First option -
Ctrl - Alt - F1
sudo service lightdm restart
Second option -
nomodeset (this often seems to be discussed as some sort of menu option)
(There's also mention of Esc followed by adding "vga = normal" before a hyphen)
There's bound to be a single solution, but it's difficult to filter them out because there are so many incidents where 12.04 seems to have black screen issues.
IMPORTANT EDIT - apparently there was a marketing decision made sometime back in the Ubuntu boot process. During startup, do you happen to notice something that looks like a sideways apartment building with an arrow pointing to a stick version of Michelangelo's Vitruvian Man? That apparently is supposed to mean "hit a key to stop automatic boot". If you do so, you can enter the old-style non-X environment, which is where the F6 option can be used.