Hi:
Just a thought but nomodeset might work-
I used these instructions the other day for Ubuntu 12.10 and it worked for me.
The newest kernels have moved the video mode setting into the kernel. So all the programming of the hardware specific clock rates and registers on the video card happen in the kernel rather than in the X driver when the X server starts.. This makes it possible to have high resolution nice looking splash (boot) screens and flicker free transitions from boot splash to login screen. Unfortunately, on some cards this doesnt work properly and you end up with a black screen. Adding the nomodeset parameter instructs the kernel to not load video drivers and use BIOS modes instead until X is loaded.
If you boot ubuntu from a livecd (or USB stick), right after the bios splash screen you will get a purple screen with a keyboard logo at the bottom.
Press any key at that moment to access a menu. Select your language with the arrow keys, press enter and you will see this menu-
If you press the F6 key, a menu at the bottom will open allowing you to set kernel options with the space bar or enter key. You can close the menu with escape key and resume booting by selecting the option “try ubuntu without installing” (please note that session does allow you to install ubuntu once you found the kernel options cured your problem).
If you need to add kernel options not provided by the F6 menu, you can just type them in at the end of the boot options line.
Important: if you select a kernel boot option from the F6 menu and proceed to boot and later install ubuntu, those boot options will NOT be applied to your installation. If you needed nomodeset to get the livecd to boot, you will almost certainly need it again once you reboot in to your fresh install. See below how to set those options on an installed ubuntu.
During the install are you manually creating your own partition and a swap space?
What distribution did you have on your laptop before you tried to install Ubuntu 13.04? Do you have UEFI BIOS?
It is possible that the graphic card could be on it's way out:-
Also, it could be your boot order.
I had to set my laptop to boot to the CD/DVD ROM drive first in order to install Fedora. The next on the boot order list in my BIOS is the HDD-