What do you mean by the "built in" admin account?
Are you referring to the hidden account, which you have now enabled?
If so you should have been able to delete the offending account through the Control Panel - user accounts.
Did you follow this procedure:
Manage another account - (then change to the faulty account) thern, whebn the window came up, you have the option to delete the account and a further query, "Delete files also" I cannot emulate this, so the wording may not be accurate. What I can suggest, if you go back into the "Global" admin account, is that you recreate your old user and go through the procedure again.