logon account problems

Xref: 127.0.0.1 microsoft.public.windowsxp.security_admin:58741

First of all, my computer is a rental. My op sys is
windowsxp-home edition.
I believe I created this problem myself. I just got the
computer and had many programs from my previous computer
that I wanted to install.
I am the only user of this computer. I began the process
of loading files using the rental agency's logon and,
belatedly, after installing many files, decided to create
my own account.
I did this, creating my own account as an administrator
but then discovered that by logging off the original
account onto my new one I lost all the work that I'd done.
I solved this ingeniously (I thought) by changing the
name of the original account to my name, thus retaing the
results of my work!
I am now trying to install and run a program that can
only be installed or run by an administrator.
When I try to launch the setup program, nothing happens.
When I right-click and choose 'run as' I get the
message: "You must be logged in as an adminstrator to run
(program name). Please log in as an administrator."
I noticed that the logon name given in this message is
the original logon name, that of the rental agency.
Evidently the computer didn't recognize my name change.
I tried setting up yet another account as administrator
but the computer still has me as the original rental
agency.
What can I do to resolve this mess?