Windows 8--"iTunes64Setup" (11.1.3) will not run/install

Question

Hi all,
I received an iPad air for Christmas today, and naturally I plugged it into my laptop (a Sony Vaio, running Windows 8.0) in order to access iTunes (we do not have wi-fi at home).  My laptop, which at the time was running iTunes 11.0.5 (I believe) said that the iPad needed the latest iTunes update (11.1.3--well, technically it said 11.1) to work. 
Well, that's all fine and dandy, but the Apple Software update program proved disappointing immediately. I checked iTunes off (99.83 MB), but not iCloud, and clicked install one item.  Now, the download always stops during the 67.80 MB mark of the download process (I have tried this multiple times--once or twice it reached an .1 MB mark, and then stopped).  An error message appears: "iTunes" has an invalid signature.  It will not be installed.  |and then| Errors occurred while installing the updates.  If the problem persists, choose Tools > Download only and try installing manually.  ...That doesn't work either.
So I go to download the 64 bit update from the Apple website itself (I use Google Chrome, by the way--and yes, IE also proved no better), and after a few failed download attempts (they said: Failed--Network error) manage to get the file labelled "iTunes64Setup."  If I click on it directly, it asks me if I want to run it (the publisher is 'unknown' apparently).  When I do, an empty bar flashes on screen (and an icon appears in the taskbar) for the briefest of moments before both disappear.
The same thing happens when I try to run it as an administrator. 
My security software is Kaspersky, and I did go check to see if the setup was allowed.  I did try to clean out my Temp folder, but that has met with failure as well (though perhaps I'm doing that solution wrong, I'm not sure). 
I did at one point uninstall my iTunes completely (and I deleted the related files) in an attempt to do a complete reinstall.  That failed as well. In fact, I couldn't even download iTunes 11.0.5 again (even though it has been working without a problem for months).  I did manage to find an old 10 point something or other version of iTunes that has installed well enough on my laptop; but you know, I'd really like for my gift to not go to waste. 
Any advice would be appreciated. 

Answer 1

I am having the same issue with Vista 64 bit: After many failed download attempts ("network error") the Progress Bar briefly appears and that's it.
Searched for solution that led me to running "Microsoft FixIt", deinstalling iTunes, Apple Software Update, Mobile Dev Support, Bonjour, and Application Support - even manually deleting common files that were left over (tough with Vista). No difference. FYI, I was able to get rid of the Apple folder in Program Files (x86)/Common File, but not in Program Files/Common Files ... but that shouldn't make a difference as I am installing iTunes64Setup.exe, right?
I even tried iTunes 10.7 and 10.6.3 from Apple's support page ... same differnce.
Had a lot of security updates on 1/22/14 (all related to Office 2007 (including SP3), though). So I tried to restore past this point, but an "unknown error" occurred and I am stuck where I am ... lovely.
So now my system is chopped and I seem to not be able to get iTunes even close to my computer ... :-(
Just Irritatedtech said: Any suggestions are highly welcome ... - Thx.