It's probably a hard disk failure since your system work perfectly well with a Live-CD. You can partially fix this by using this command from the Live-CD :
sudo e2fsck -cy /dev/sda1
You have to change /dev/sda1 by the name of the partition of your system (and make sure it is not mounted), if you don't know what is it, you can use :
sudo fdisk -l
Which will show you all the partition on your system. This operation will take a long time and basicilly will add dammaged sectors of your partition to a list so that the filesystem will don't access them again (that will prevent the system from crashing). Since the data on damaged sector will be lost your system may not start even after the fix, in this case save all your important datas with the Live-CD and reinstall on the fixed filesystem (don't format or you'll lose the list of bad sectors and you may crash during the installation). You should do it to every partition of your damaged disk.
In any case make sure to save all your important datas.