I would say the application itself is not actually being fully unistalled. Here is a solution I have used with success with some of the users at my job.
Warning! the following fix involves using a script that modifies your registry. I take no responsibility if you screw it up. I also recommend making a backup of your registry by going to Start>Run, type Regedit and hit enter. Then highlight "My computer" in regedit window and go to File>Export. Save as "backup" or something similar on your desktop, my documents, or whatever. Then if the process does something funky to your computer, you can just double click that file, click "yes" and it will restore what you have screwed up.
So that being said, try this.
1. First run the uninstaller for iTunes/Quicktime to the best of your ability. If it fails or errors out, fine, just hit ok and continue with this fix.
2. Next, download and extract the following application to a folder called MSIfix(or whatever you prefer) on your desktop, c: drive, or wherever you can find it easily. app:
http://www.helpware.net/downloads/MsiFix.zip
3. Now, run the MsiFix.exe in that folder and select tab #2.
4. You will see a list of apps like in "add/remove programs." Find iTunes, select it, then select the next tab.
5. On that tab click "search." You will see a list of registry entries for the apps installer.
6. Click "remove" and accept any warnings that might pop up. Repeat the process for the Apple Updater and Quicktime as well.
7. Now that your computer thinks the application is non-existent on your drive, proceed with a clean install from the latest version you can download from Apple.com. Just be sure to grab the iTunes/Quicktime bundled installer.
8. Once it is installed run it and see if that solves your problem.