You should have received an Office installation disk with your system. When it prompts you for the original installation location, insert the disk and point it to that drive. If that does not work, uninstall office and reinstall it from the disk. The key is on the disk envelope.
There is no way around this without a CD. The original installation did not install Outlook completely to the hard drive, so it is more of a partial installation to save hard drive space. Try googling for Office 2003 CD download, you might get lucky and find one to download without a CD key.