You can face this issue in two conditions.
1. Those who have installed ubuntu 10.04 might encountered this problem. The screen goes blank just after grub (may be after bios startup, if grub timeout early).
Please follow the steps below to fix it.
Press e on getting the GRUB bootloader(if not getting grub, press and hold shift key to get grub).
Go to the line which says ‘quiet and splash’, delete thesee words and type in ‘nomodeset’ in their place.
Now press Ctrl + X to boot
Now login to your Ubuntu as usual.
If you have a Nvidia graphics card, this may be the issue with it,
Now goto System->Administration->Hardware drivers, and select and activate the nvidia current driver if you have an nvidia card. The driver will be downloaded and activated automatically, and you will be prompted for a reboot.
2. Blank screen on bootup after Upgrade from 9.10 -> 10.4,
A solution for this is not found, i am on it. Maybe upgrading to a new kernel will do it.