Assuming it's just XServer Failing
Try this first, after a minute of that - hit Ctrl+Alt+F2.
That might drop you to a TTY screen where you can login text-based and do the updates/installs there.
Assuming it is the Graphics
(which would surprise me, normally if that's the case it dumps you into TTY)
Boot into a liveCD (whatever you installed from might be the best). Make a place to mount the partition of your linux device and then you can chroot in and install the graphics you need to test if that is the issue. Chroot should be installed by default on most liveCDs.
1) Boot into the liveCD (should put you in as root).
2) Make a mount point you know of for your local disk
mkdir /mnt/brokenlinux
3) Find the partition of your linux drive (outputs all drives and their partition info)
fdisk -l
4) Mount the linux installed partition to the mount point you created
mount /dev/sda# /mnt/brokenlinux
5) Chroot in and then do the updates and such.
chroot /mnt/brokenlinux
I don't know which linux you're on, so I can't tell you what to update. I know arch is pacman -Syy && pacman -Syu, debian based is apt-get update && apt-get upgrade.
Make sure your graphics card is recognized and then find which drivers you'll need.
lspci | grep VGA
Maybe it's actually GRUB not seeing the right partition
If you know the partition, during boot at grub, hit "e" for edit and check that it's looking at the right partition.
I don't recall 100% (I use syslinux), but I think it looks like (hd0,#). If you try that and it fails, nothing is saved so rebooting will revert to default.
If that is the issue, however, when you get into linux just edit /boot/grub/grub.conf with the correct #.
Best Answer
Yep, it was the first Linux distribution I tried. I still have the CD-ROM somewhere.
I had to recompile the kernel in order to use the printer port. It was occupied by some TPC/IP over printer port (!) device.
Update: I found it. Text on the CD-ROM (for reference):
An upload may follow.