If it did, just start all over again by formatting the drive and installing 10.5.x again.
This time use your own name to create the an account.
It's possible that whoever installed OS X prior to you purchasing the Ti, did not do the job correctly and now most things belong to that original user.
I recently purchased a used 15" PowerBook Ti 1.0GHz with a fresh install of OSX 10.5.8.
Even though I am logged in as Administrator it will not allow me to rename folders or to delete some files. When trying to rename a folder, for example, it displays, " You do not have sufficient access privileges to rename the item."
I have run the Disk Utility to repair permissions but with no improvement.
When I Get Info on the folder, it says I have Read and Write permissions but I cannot change the name in the Get Info box, either.
It there something I am missing (probably).