Since you are on a HOME system, things are different, if you were running the PRO version then YES, you could login to the "Administrator" account in the normal mode. This is why it is hidden and TweakUI was set to make the "Administrator" account visible for those that require "IT" support for that machine. On a Pro machine with the Administrator account hidden, all one has to do is use "Ctrl-Alt-Del" while at the "Welcome Screen" and the standard Win 2000 login pane would open. Here you could type in the account name "Administrator" and the required password. By the way the HOME version does NOT require a password where the Pro version does.
In the NORMAL mode you have one and only one Admin type of a account at this time unless you have made more since your last post. You MUST have at least ONE admin type of an account in the NORMAL mode at all times now that you made this account for the normal mode use, you can NOT delete the new one you have made until you make a addition one in the normal mode, which will get you nowhere.
When in the safe mode the ONLY account you can use is THE "Administrator" account. This account now that you have added a admin account in the normal mode, can NOT be used any where except in the SAFE MODE.
While in the safe mode you may be able to move any and all of the files under Cocuments and SettingsAdministrator to a different folder that any account in the NORMAL mode can access.
<hr>Also, even though I have the two admin accounts, it won't let me delete the non-Safe mode one (or the Safe mode one for that matter).<hr>This is correct, you can NOT do what you want to do and there is NO why other than a clean install to the OEM factory settings and start over with NO user account and then you will NOT be able to add any other accounts, without getting into the same mess you are in now.