That update may have been the one for Lion and Mountain Lion, not Snow Leopard. If so your system has been garbaged, and you will have to reinstall Snow Leopard. The correct update is Security Update 2013-003 (Snow Leopard). I suggest you do the following:
Repair the Hard Drive and Permissions
Boot from your Snow Leopard Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer.
If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.
Then reinstall the security update from the above download.
That does not work with an external drive. Startup this way:
Boot Using OPTION key:
1. Restart the computer.
2. Immediately after the chime press and hold down the
3. Release the key when the boot manager appears.
4. Select the Snow Leopard DVD's disk icon.
5. Click on the arrow button below the icon.