Before we go "hip deep" into this troubleshooting - do you have another hard drive to replace this one with? Lets eliminate this as a issue. Also in the bios do you have a setting for raid - sata ect? Could you take a picture of the bios screen of this setting and post it. Also the sata setting page.
I've been researching the chipset "ATI All-In-Wonder 9600", this is a tv tuner card. It should work with wheezy it uses the driver "radeonfb". The "driver" is part of the wheezy distribution. You do not need to install it.
Read this posting here: it has some relevant information.
forums.debian.net/viewtopic.php?f=7&t=91510
For troubleshooting purposes I would suggest;
Check bios for onboard graphics setting; if you have onboard graphics -remove the Radeon card
Check bios for sata settings or raid settings disable raid settings if found.
Swapping the HDD for another to test, ensuring its not a hdd pending failure.
Since you can boot into the live cd that would suggest the video card is ok, however during install Linux must detect and set a proper configuration. Hence the removal of the card to eliminate it for now.
Here is how to enter the nomodset to grub:
askubuntu.com/questions/38780/how-do-i-s...ady-installed-ubuntu
Let me know how things go!