Are you logged in as a user with Admin privileges?
Launch Disk Utility, select the startup volume and click Repair Disk Permissions button.
If that doesn't help, start the computer up from its install disk, go to Menu>Disk Utility select startup volume and click Repair Disk button.
If the updater install via "Software Update" is not working for you, download updater from apple.com and run it manually. You should be getting the 10.5.6 "Combo" updater since you need to jump from 10.5.3 from 10.5.6
http://www.apple.com/downloads/macosx/apple/macosx_updates/
Info on the combo updater
http://support.apple.com/kb/HT3194
You do have a backup, right?