And old age made me miss your reply so sorry I'm a day late.
I've never known a hidden system Administrator account in XP before but it is hidden by default in Vista and Windows 7. Please don't think it insulting if I ask are you certain you have XP and were you definitely in Safe Mode when the screen failed to show the Administrator logon icon?
If you're sure about both, this is quite a problem and you would need to use a Linux Operating System to tunnel in and retrieve your personal files before reinstalling XP.
First, and if you have a Windows XP CD, pop it in and boot from it then select the first Repair option? At the Command Prompt on a black form, type chkdsk /r (including the space) then hit Enter and a five stage process will run which might help fix this.