I ran into the same problem, but I think I have the solution. First, the problem isn't with iTunes, its an access problem with Windows XP. I tried to run the iTunes program from the Program Files, and I received an "Access Denied" error.
If you try to open the Program Files in My Computer\Local Disk(C:) and receive an "Access Denied" Error, that is why you are receiving a "shortcut problem/Fatal Error during installation".
Here is how I corrected it:
1) Shut down the computer and restart it in "safe mode". I had to look up how to do this, but I pressed F8 when it was restarting and I highlighted the "safe mode" and started the machine. The icons will be large, but ignore it.
2) Open a user that has administrative access -- I used the one user that has access to itunes.
3) Go to My Computer\Local Disk (C:) and right click on the "Program Files" folder. Select "properties" at the bottom.
4) Go to the Security Tab
5) At the top you should see one or two users that have access to the Programs File. One will be the user that itunes works on. Click Add, then click Advanced, then click Find Now.
6) At the bottom should appear a list of users. Select a user on which itunes doesn't work. Click Ok, then click OK again.
7) Give that user full access to the Program File by putting a check mark in the Full Access box.
8) Repeat for the remaining users.
9) Restart computer in normal mode.
10) Go into a user that had problems and click the itunes icon, and it should run.
It worked for me, I hope it works for you.