I think the best answer is buy a new video card unless this is a laptop.
Anyhow, looks like this link provides the best answer, but it is for 10.04 and needs to be modified to work in a later release. I have not had to do this before, but here's what I came up with.
I of course have no way to test this. So this could be a fix or this could totally bork your system.
sudo cp sis671_drv.* /usr/lib/xorg/modules/drivers/
sudo service lightdm stop
Switch to tty1 by pressing Ctrl+Alt+f1
service lightdm start
sudo mv xorg.conf.d.new /usr/share/X11/xorg.conf.d
sudo service lightdm restart
echo blacklist vga16fb > /etc/modprobe.d/blacklist-vga16fb.conf
I would suggest waiting for others to comment on this before trying it on your system.
Edit: Had a typo