I have installed Lubuntu 13.04 on a Dell Inspiron 1501 laptop, rebooted the machine and encountered this problem. I edited the GRUB configuration to remove "quite splash" and enter "nomodeset", updated grub, and everything was fine. I could reboot the machine without any trouble.
However, if I unplug the machine, wait a few seconds, and plug it back in, the problem with the colored lines comes back and nomodeset no longer helps to solve the problem. I tried using radeon.modeset=0 instead of nomodeset and that also works on multiple reboots until I unplug the machine and plug it back in. I was finally able to get around the problem by entering "radeon.exapixmaps=0" instead of radeon.modeset=0. I suppose I kind of made up that boot option using some information from an Arch Wiki page. This would work throughout reboots and even if I unplugged the laptop. It was working fine for quite a while.
A few weeks later, I had some unrelated issues with the Java iced-tea plugin, and since 13.10 had just come out, I thought I would try upgrading. So upgrading didn't fix the problem with Java, and after unplugging the machine and trying to use it later, I was back to this problem with the black screen and colored vertical lines.
I am completely out of ideas on what to try. It took me a week to figure out how to get it working the first time, but the solution I had isn't working anymore.