What you are calling 'graphical corruption' is a result of the /etc/X11/xorg.conf file not being set up correctly. This file contains information about the video hardware, the monitor(s) mouse and keyboard.
No reason why linux can not be made to work with this configuration.
For this file to be correct, the hardware has to be detected properly. It would appear this has not happened, in this case. Detection improves all the time, however, understand there are thousands if not millions of video card, monitor combinations.
With that said, to fix this, we need some information, and you need to provide it, remember we can not see your system and its hardware.
What distro are you trying to install? Include the version.
Next, can you get a usable terminal window? The graphical part that is not working is provided by a server called the X-server. To see if you can get a terminal to log into, use the key combination of Ctrl + Alt + f1 ( all together ). That should get you to a log on terminal.
Once there, log in. You should have created a user and password during installation. You should also create a root password.
Run the command 'lspci' ( Only type the characters between the quotes ). It should list all devices connected to your PCI bus. Cut and paste the data to this forum.
If you can not get that to work, post the make, model of your laptop. Look for that information on a sticker, usually put there when manufactured. Then we can look up the stuff we need on the makers web site.