when you download Process Monitor, it will be a compressed folder
open the zipped file
copy the main file to your desktop
open that main file
accept the EULA
it should automatically start gathering data (tons of data)

un-install iTunes while Process Monitor is gathering data

Once you see the error that the iTunes uninstaller cannot remove the shortcut, stop gathering data via Process Monitor. You can move your mouse over each of the icons on the toolbar within Process Monitor - read the tooltips to see what each one does. One of icons is a magnifying glass and it has a tooltip of Capture (Ctrl-E). That is the one that stops the gathering of data. You can see me do this in the videos that I linked too.

You can now dismiss the error presented by the iTunes uninstaller and do whatever you want to finish that un-install process. You can manually delete the desktop shortcut.

Back to Process Monitor: there is a funnel icon on the toolbar to filter the data; click on that funnel.

In the filter window:
change the first drop down menu from Architecture to Path
change the next drop down menu from is to contains
the next drop down menu is now a field that you can type in
type iTunes.lnk into that field
select Add to add the filter
select OK to exit the filter window

download and open the compressed folder that I attached to post #34
double click on the only file in that zip
that should open another Process Monitor window and a filter window
dismiss the filter window

you should now have two Process Monitor windows open
compare the filtered lines on each
the data gathered from your computer should show an error somewhere