(Like many of my technology postings, this is really here for my own notes on problems I run into, the solutions I try and what works when. They are updated as I learn.)
After uninstalling Itunes with Revo Uninstaller, I followed these steps from Gheeda Al-Zubaidi.
To solve this issue:
1. I right clicked the installation file
2. Went to properties
3. Clicked unblock
1. From the start button, searched for "uac"
2. Clicked "Change User Account Settings"
3. And dragged the bar to "Never Notify" (needs restarting)
4. After restarting, I ran the installation as administrator again, and it worked!