My iPhone 5 will not turn on or connect to iTunes?

I bought a iPhone 5 roughly a month ago. Today it stopped working and i'm not sure why. The screen does not turn on and it does not acknowledge it is connected to the computer. I have tried to charge it multiple ways and it is not the cord since it will charge my friends iPhone. I have also tried to hold the home and power button for 30 seconds as everyone tells me to but it still does not turn on.

IMessage is not working with iOS 6?

On Friday, I got a new iPhone 5, well, later on after I had synced it to my computer and everything, I decided that I would turn on my iMessage and FaceTime. I went to iMessage in my settings and it said, "waiting for activation," so I tried to activate it, it said, "Could not sign in. Please check your network connection and try again." I had 4G and four bars of service. Why won't it work? I've "reset all settings" like twice.
Then, when I open Snapchat, an alert pops up saying," Connect to iTunes to Use Push Notifications. Snapchat notifications may include blah blah blah." No matter how many times I press OK, it will NOT go away.
The same thing happens with a lot of my other apps every time I open them, but they go away after I press OK. I'm just not getting any notifactions which is very annoying.
Can someone Please help. I've synced my phone countless times and looked on so many forums and nothing has worked.

Added (1). There isn't anything wrong with my backup?

How to get rid of other space on iphone? - 1

Recently my "OTHER" section on my iphone is taking up 28.33GB of my 32gb (it didn't built up over time, it was just all randomly there one time I tried to sync my iphone). Now i can't sync my music. There's no way it's the iOS data because it's almost the entire storage on my phone!

How much will it cost to get a new verizon plan?

So I have had my phone for almost 2 years, it is a basic phone. The phone just stopped working and I can't make any calls on it. My mom said she wasn't going to get a new one. She insists i pay for everything. I have a job, but at pizza hut and i get paid every two weeks. I also have gas and car payments. I want to get the iPhone 4. I can get the phone itself for free. I just want the basic usage/data plan for it, nothing spectacular. I want to know could i get my own bill at age 16? And how much would it cost? Does it cost anything to set it up?

Syncing iPhone with new computer? - 1

I downloaded some ringtones that I would like to put on my iPhone, and I need to do this through iTunes. I connected my phone to my desktop computer's iTunes, but the ringtones are on my laptop's iTunes. My desktop computer doesn't work so I can't put them on that way. When I go to put them on on my laptop, a message pops up when I click sync. It says that I can only sync with one library and asks if I want to erase my phone and sync with that library. My question is what would it erase? Would it erase all my apps and info on there? Or would I just lose my music?

Problem trying to update iOS 7 Beta? - 1

I'm having some trouble installing iOS 7 unofficial beta there was a leak and I've done this before but for some reason this time I'm getting an error saying The iPhone ___ could not be updated because the firmware file is not compatible. I don't understand why this is happening someone please help. (I do have a developers account but that doesn't work either.

Is straight talk overall a good service for iphone 5?

I've been wanting to buy an iphone 5 in straight talk, because everything is unlimited and its affordable. But before making a mistake i wanted to make sure if it has good coverage, reception, etc. Is it unlimited on memory. All that good stuff. I heard they kick you out if you go over 2MB. Something like that. I usually don't travel much and it says it only works in your zip code area. I'm always here so that's pretty good. Just wondering about everything basically.