Yes, most people are able to get iTunes updated following the advice in Troubleshooting issues with iTunes for Windows updates.
When you wiped off the old version of the iTunes application did you also delete the installation folders as named in the second box of the user tip? If not the roll back is likely to be unsuccessful. You may also need to roll back the library database too. Other tips include temporarily disabling AV software, using a fresh administrator account for the install, or the segment on breaking down the installer into separate components and adding them one at a time.
Quite why things go wrong is unclear, and the causes and effects seem to vary quite a bit, but the overall recovery process should work. That said I would wait until you have repaired your system before trying to update any other computers in the household.
What is the exact text of the error message that you get now? Several have been mentioned in the context of this thread.
tt2