What is the problem with my OS Windows XP when a file called "My
SYSTEM.INI" keeps the program from starting? What steps should I take
if the problem should arise?

You can check out these discuss for clarification... 

http://www.computing.net/windowsme/wwwboard/forum/44549.html

Regards.

You can replace the system.ini, manually, or by a registry restore, or
a system restore.

To the manual way first. Start, Run, Type; sysbckup Press Enter. This
will open a window, and in that window you will have files {rb001.cab,
rb002.cab, ect.}. Right-click one of these, and click Explore. Now, in
the right side you will see "system.ini". Extract one, to your
desktop, open it and compare to the one you are using. Can even use
that one, instead of the one you're using. Can even extract one from a
restore point, if so inclinded. Nevermind that for now ;-)

Start, Run, Type; scanregw /restore Press Enter. Now choose a
good/started registry backup, to restore. Do this, when you're ready
to restart the computer. As it will have to, to restore the registry,
and files.