I had this problem. It took me about a night of work scouring various help pages on the internet, but I solved it. The issue is likely that your Windows is not up to date. Go to Start, then All Programs, then Windows Update. Try to update it. If you're like me, you get an error message (80070422, to be precise). Microsoft Help says you have to go into Services (Start, then type Services in the Search bar and click on the "Services" button) and insure that Windows Update is on Automatic, and is Started. That didn't do it for me, but I found a thread somewhere (that I unfortunately cannot find again this morning) that said that you have to also set Windows Module Installer to Automatic and Start it as well. I did this, and was able to update Windows.
Once I installed all of the updates, I uninstalled everything I had on the computer from Apple, and reinstalled iTunes fresh, and it worked. It's apparently a somewhat common issue; no word on whether or not malware was the cause. Anyway, if you're still looking for a solution four years later, I think I found it. Even if you don't have the same error I did, just do whatever you need to do to get Windows Update working, and then try installing iTunes after that.