Here’s the solution (inspired by Crusisx!) that worked for me:
1) Install iTunes as you normally would.
2) When you get the error message "iTunes errors occurred during installation before iTunes could be configured" do not click finish and leave that folder up,
3) Now go to C:\Users\Your Username\appdata\local\temp
(If you can’t see your appdata folder when you are in your username folder, just click on VIEW in the menu bar and then click on “Hidden Items” and it will appear as if by magic)
4) Inside the temp folder, look for a file called IXPXXX.TMP (where XXX means any 3 numbers (but the X of IXP is really an X!) (eg: IXP651.TMP)
If there are a couple, find the one that is most recent by right clicking it and choosing properties to find out when it was created.
5) Open the folder and inside you will find some files - they are all the installation packages.
6) Copy all of those files and paste them into a new folder wherever you like.
7) You can now click finish on the failed iTunes installer
8) Now, open the new folder where you copied the files and double click the itunes setup file.
You should now find iTunes installs correctly.
Thanks again, Crusisx!