change to the media directory (where our drives should be)
# cd /media
Create a new directory called Ubuntu (We will use this to mount our boot drive too)
# mkdir ubuntu
Mount the boot drive, you will need to replace X with the correct letter
# mount /dev/sdaX /media/ubuntu
Mount some other required locations
# mount --bind /proc /media/ubuntu/proc
# mount --bind /dev /media/ubuntu/dev
# mount --bind /dev/pts /media/ubuntu/dev/pts
Run chroot, using this command and we are now root as if we had booted from the boot drive and not the liveCD:
# chroot /media/ubuntu
Your now in your Ubuntu system as root. If your unsure precisely why your system won't boot then running an update is usually a good place to start. Good luck!
# aptitude update