To backup your IE favorites: File>Import and Export ... and tell it to export your favorites. Put the resulting file (called bookmark.htm) on your external drive and import it later the same way.
For backup of Outlook 2003, read http://support.microsoft.com/kb/287070
Do I understand correctly that until now you didn't do such a backup on a regular basis? It's much safer to do that, and with a 500 Gb external drive you'll have no problems to store it.
Hope this helps.
I have been told by my engineer that my hard drive must be replaced. How can I save my e-mails from Outlook 2003, and My Favourites list from IE, so that I don't lose them? My CD//DVD writer doesn't work, but I have a 500gb portable external drive.