ITunes not working/iPhone iOS7 won't update

Question

Alright so apparently all of Apple software has decidede to crap out on me that I'm starting to regret spending money on this phone. A software update came out, iOS 7.1 so I very stupidly decided to download. I say stupidly since it seems like that's what started everything.
Obviously, to download it you need to be over a Wi-Fi connection. My Wi-Fi connection is great; I use it for everything (Netflix, email,i tunes, you name it). Strangely it didn't work like every other time. It was just stuck on "estimating remaining time" and after 5 minutes I got a failed to download message.
Weird, I thought, so I decided to test if the Wi-Fi was working. It was. I was able to load up any app, except for two things. iTunes and the App Store. None of those two work on my phone over Wi-Fi, I just get a "cannot connect to store" message. Why? Who knows, because apparently Apple thinks you're suppose to figure it out yourself why it can't connect instead of giving a diagnostic.
Weird, I thought again, so I decided to just connect it to my windows laptop, download the update through iTunes and install it from there. Sure enough, when I connected my phone and I loaded up iTunes, it immediately let me know there was a new software available for download so I went on with it so I could it all over with.
Nope.
While being stuck on the "contacting iphone software update server" for a SEVERAL minutes, I noticed on the top the "accessing itunes store" message was also stuck. Eventually, iTunes gave me an error: "There was a problem downloading the software for the iPhone. Make sure your connection is active and try again." Huh? I use my wi-fi every single day, it's never failed me. It's working RIGHT NOW. I can access the internet PERFECTLY. I can access any internet related apps on my phone through wi-fi as well. Heck, it's ALWAYS worked. I've bought, downloaded purchases and updates normally through this wi-fi connection ever since I bought the phone. Everything works, except itunes/app store on my phone and now as well as iTunes on my laptop.  It's just stuck on the "accessing itunes store" message and I can't even log in. Every time I enter my ID and password, nothing happens, the box disappears and when I click sign in again, it asks me again for my ID/password. It never registers it's just stuck on a loop.
So now, I'm not too concerned about itunes/Appstore not working via wi-fi on my phone since they still work properly if I use my cellular data instead (but obviously I can't download the update since I NEED to be over wi-fi). What concerns me is iTunes being completely useless. I've tried just about everything I've read on several posts in this site, including the "netsh winsock reset" trick that apparently was very helpful to many people.
Anyway, if anyone can help me how to fix this, I'd appreciate it. And if someone can tell me exactly why this happened would awesome as well; I need to know if I did something wrong that screwed this up so I can make sure I don't do it again.

Answer 1

While being stuck on the "contacting iphone software update server" for a SEVERAL minutes, I noticed on the top the "accessing itunes store" message was also stuck. Eventually, iTunes gave me an error: "There was a problem downloading the software for the iPhone. Make sure your connection is active and try again." Huh? I use my wi-fi every single day, it's never failed me. It's working RIGHT NOW. I can access the internet PERFECTLY. I can access any internet related apps on my phone through wi-fi as well. Heck, it's ALWAYS worked. I've bought, downloaded purchases and updates normally through this wi-fi connection ever since I bought the phone. Everything works, except itunes/app store on my phone and now as well as iTunes on my laptop.  It's just stuck on the "accessing itunes store" message and I can't even log in.
With that cluster of symptoms, I'd start with the following document:
Apple software on Windows: May see performance issues and blank iTunes Store
(If there's a SpeedBit LSP showing up in Autoruns, it's usually best to just uninstall your SpeedBit Video Accelerator.)