IOS 7 won't show up on iPhone 4?

I updated my iPhone 5 today after school. Everything went smoothly. Then when my mom got home from work she wanted me to update her phone too. It's an iPhone 4. The update was available so I clicked download and install. Everything was working, and when it shut off to restart after installing, nothing changed. It's still at iOS 6.So I tried it again, both times very time consuming, it said it finished installing and restarted- still nothing. Has this happened to anyone else? What do I do to get it to update? She has enough space on her phone as well.

How to update to iOS 7

Okay, so iOS 7 has been released today for a fact, I know September 18th is the date, and my friend sent a snapshot of his own phone having "iOS 7 update" on his general > about > Software Update.
we BOTH have iPhone 4. He already updated to iOS 7, and I'm trying to now. I keep going to "Software Update" and it keeps saying 6.1.3 is up to date. So I try iTunes and I have the latest iTune Software and I know because I just checked myself. So I click on "Update" on iTunes and it says it requires 11.0.5, which I have I just checked. And it keeps telling me I need it to update to iOS 7.
I'm guessing that so many people are updating they're limiting it right now, and maybe in like 30 minutes so many more people will continue to try.

Why is it doing this?

More Info:
Me and my friend both had a jailbroken iPhone, we both restored from factory settings, but I also restored from my latest iPhone backup. My iPhone is no longer jailbroken.

Added (1). My Carrier is Verizon.

What do I do if my iPhone is not turning on?

I shut off my iPhone since one of my apps was not opening after I downloaded iOS7 then when I tried to turn my phone back on, it is staying on the apple logo and not turning on the phone. The apple logo disappeared for a second then went back to the logo. Its been on this for 10 minutes now. What can I do to fix this? I plugged my phone into an outlet and my computer but nothing is popping up or happening

Why does my iTunes have more storage than my iPhone?

I'm trying to download iOS7 on my iPhone 4 8gb but it said I needed 2.9gb to download it. I cleared 2.66gb on my itunes on my computer but on my phone it says i only have 2.7 and i have almost everything gone! No pictures, less than 230 songs and only 3 apps! Why isn't my storage capacity the same on both devices?

What can I do if my iPhone is not turning on?

I shut off my iPhone since one of my apps was not opening after I downloaded iOS7 then when I tried to turn my phone back on, it is staying on the apple logo and not turning on the phone. The apple logo disappeared for a second then went back to the logo. Its been on this for 10 minutes now. What can I do to fix this?

Added (1). When I plug my phone into my computer, iTunes isn't even recognizing its plugged in

Iphone won't finish restoring?

I have ben sitting here for hours since i just bought a iphone on ebay and it was in recovery mode so i hooked it up to tunes and clicked restore so when my iphone loading bar was 99% full and only 1% is left and it won't move i restarted itunes and phone and tried again but no matter what i do i get the same out come every time so i'm lost and don't know what to do now