ok I would check /var/log/syslog and dmesg which will display kernel log.
wstein@valhalla:/home/wstein# sudo less /var/log/syslog
wstein@valhalla:/home/wstein# sudo dmesg
What a graphic-card are you using? Nvidia, Ati or Intel. I assume that drivers faild for install. Have you configured a framebuffer for grub? You can try an apt-get install -f which should try to repair broken packages. Hope that helps. Don't worry :)
So as you said in your comments it seems that the NVIDIA drivers failed for installing. As far as I know Ubuntu the NVIDIA modules are compiled against your installed kernel when you are installing the packages or a new kernel - since the modules are also provided to the ram disk grub is updated as well when you installing the drivers.
For Example, when I installed the newest kernel - which was not the Ubuntu 14.04 default - because I needed a patch for my BT adapter the installation went find but when the system booted I had the same problem as you. The reason was that the nvidia drivers could not be compiled against the new kernel. I saw that when I removed the nvidia packages and installed them again. For that you have two possibilities.
1) This example is for my system, you have to adapted the installed packages name. It could be that a reconfigure is not enough but you can try it:
wstein@valhalla:/home/wstein# sudo dpkg --get-selections | grep -v deinstall | grep
wstein@valhalla:/home/wstein# sudo dpkg-reconfigure nvidia-304-updates
2) A way that should work (you also need to adapt it to your nv-package):
wstein@valhalla:/home/wstein# sudo apt-get purge nvidia-304-updates
wstein@valhalla:/home/wstein# sudo apt-get install nvidia-304-updates
It could be that this will work out of the box, but if not you will see what the problem is and can react over that. It could be that you might have to upgrade your system to the 14.04 LTS version if the drivers are not compatible with your default kernel. But don't worry. Try this solution for the moment and when it does not perform we'll take a look at it again :)