Backup files off the computer (not TimeMachine) and disconnect.
If you have TM, or a option key bootable clone use that to erase and restore from.
If not, c boot off the 10.6 disk, use Disk Utility to >Repair Disk and Permissions, (do not format or erase!!) and simply re--install 10.6 (doesn't touch files or most programs, but backup files off the machine regardless)
Note: If Disk Repair gives a error that is not repaired, then you have to consider erasing the drive (with Zeros) and try reinstalling 10.6 fresh or replacing the drive.
Reboot and log in, update to 10.6.8, it should not include the security update at this time (second pass it might show) because it was just released and they might need to pull it. (they need to pull it)
When you reboot, make sure to reinstall any programs that installed kext files into OS X, you'll know, they won't work.
If you get gray screen, hold the shift key and update your installed software so it's compatible with 10.6.8.
Learn how to clone here
http://www.bombich.com/get_ready_for_lion.html
TM help here
http://pondini.org/OSX/Home.html
Learn how to make copies of your 10.6 disks here
http://www.walterjessen.com/make-a-bootable-backup-snow-leopard-install-disc/
Learn how to make a bootable SL USB
http://www.maciverse.com/install-os-x-snow-leopard-from-usb-flash-drive.html
Learn which programs ARE NOT compatible with Lion
http://roaringapps.com/apps:table
Long live the Snow Leopard. 🙂