I had a similar problem last week, although with different messages along the way, but the net result was the same, I couldn't reinstall itunes. I got in touch with Apple Support, and while they were friendly, they offered no specific help, and pointed me towards the Support communities, etc. I read quite a bit of material, and tried everything I found, but nothing worked. What finally worked for me (after quite a few hours) is the following:
I installed and removed iTunes 10.4 several times, but received errors regarding Apple Application Support and Apple Mobile Device. In the last instalation, I received a message to abort, retry or ignore, I punched "ignore", knowing that the installation wouldn't work, but so as to be able to remove the different applications (completely) after.
Using the Apple Support document about removing iTunes, http://support.apple.com/kb/HT1925, I used Revo Uninstaller instead of the Windows Control Panel (see the first step in the document), to ensure I uninstalled every little item in every application. There is a freeware version on the Revo SW page, http://www.revouninstaller.com/revo_uninstaller_free_download.html. I then followed the instructions given in the second step about verifying the disinstallation.
At this point I emptied the trash and rebooted, then ran spyware and clean-up programs I had seen mentioned in different documents. This document, https://discussions.apple.com/thread/2726830?start=0&tstart=0, refers to a problem you don't have (I did, not with Bonjour, but with Apple Application Support), but gives excellent information, specifically about the Windows Installer Clean-Up Utility (see comment from b noir, Jan. 2011 2:32 pm), and about AVG PC Tuneup 2011 (see comment from bossross, Apr. 12, 2011, 2:38 p.m.). I found and ran both programs. In the first, apart from deleting pertinent entries, I also removed two blank rows that appeared in the list, and with the second, I simply ran it as a clean-up measure (without the forced installs mentioned by bossross).
I then followed the third and last step in the document mention above
(http://support.apple.com/kb/HT1925), but following suggestions I saw in other documents, I did not run iTunesSet.up.exe, rather I unzipped it (using 7-Zip), and installed each individual program. I didn't keep the link, but whoever mentioned this method also said that it was important to install the programs in a certain order, which happens to be the exact reverse of how you are to remove programs as per the Apple Support document about removing iTunes, eg. (1) Apple Application Support, (2) Bonjour, (3) Apple Mobile Device Support, (4) Apple Software Update, (5) Quicktime (6) iTunes. In my case, the 6 installations worked and I was finally (and thankfully!) finished. Certainly, doing it this way, application by application, you will detect exactly where the installation is failing, if it doesn't work for you.
Hope this helps!