Itunes Library Transfer Problem?

Last week I broke my laptop, which had my complete iTunes library. Now I have to use the home computer but when I try to transfer all my music from my iPhone to the my new library, only the music I purchased from ITunes will sync. My old iTunes library was on an older version of iTunes, while this one is up to date. There's a tab that says "on this iPhone" that shows all my apps and music but for some reason it won't transfer to my current iTunes library. Is there anything I can do to get my iPhones information to transfer to this new library?
Thanks

Addition Information
I have a 4th generation IPhone
This computer has no other iTunes libraries on it

How to activate seconhand Iphone 4s without apple ID?

I just got a secondhand iphone 4 I have no contact whatsoever, with the owner

The problem is I reset the phone so it could delete all of the previous persons information
and The phone is now blocked and I don't have a sims card since the phone was sent to me without it, to my country
and so I tried with a friends sims card and it worked but now it turns out that I need the Apple Id
I'm not going to Jailbreak it(if thats even possible at this point) but if I were to jailbreak it,
would it still be able to be used as a phone?
-Thank you (:

Added (1). Actually I think its iphone 4
and IOS 7.1? I think?
I'm really not sure at this point

Added (2). Also the top button is broken won't work at all

Switching to a basic phone from an iPhone?

Long story short, I broke my iPhone 5c. It was still under the 1 year warranty, so Apple is going to replace it. However, they didn't have any in stock at my local Apple Store, but they were going to get a shipment in 3-4 days. I still have an old basic flip phone, so would I be able to switch to that for the next 3 days and then switch back to my iPhone? Would my Verizon data plan affect this at all?

My spektrum case didn't come with a screen protector?

I recently bought a spektrum tuff case for my iphone 4. It said on its box that it comes with three pieces. But I only got the case and the rubber part. There was no screen protector. Did I get ripped off? Or is that on purpose?

Game weed firm on iPhone?

Hi, I play the game weed firm and one of my tasks is to buy a safe of someone called lee but how do I go about buying it like where is he to buy it haha?

Weed Firm Hacks or Weed Firm Cheats? - 1

Anyone got one that works? I've tried a bunch of weed firm cheats but all of them seem to have errors. There's was 1 weed firm hack that i had last week but it was patched unfortunately, and i'm about to be out of cash and running low on weed. Does anyone got something for iphone that can cheat weed firm app? Please ne help

Added (1). ya very nice. Thanks to http://allgamescheatsandhacks.com/weed-firm-hack-cheats/

Why does my iPhone 5 only charge when it's off?

The charger was working perfect until I plugged it in when my phone was dead…

My phone took so long to turn on, probably close to 20 or 30 minutes, and it was charged to 3% but when it turned on it wouldn't charge.

I thought my charger broke so I tried my sisters but that one didn't work either.

Do you know how I can fix this or what's wrong? Please answer!

How to get rid of Onavo Protect's VPN on my iPhone 5?

Hi. So lots of people at my school has the ' Free VPN -Onavo Project ' app from the App Store to get VPN so they can get on Instagram and Twitter which is blocked on our school Wi-Fi. My friend got it on my iPhone 5 about 5-6 days ago. At first, it was working great. Now. Not so much. Now I can't use any of my apps needing Wi-Fi ANYWHERE with any kind of Wi-Fi. Apps such as Instagram, iMessage, Facebook, Internet, and more won't work. It also freezes up my phone and kills the battery.

How do I get rid of it? After I got it on I deleted the app because I found no use in it, but everyone says you need the app to delete it. I've tried to re-download it but it won't let me, since App Store doesn't work with it. I was thinking about going to the Verizon Store to see what they can do, but Onavo IS an illegal app:/ and plus, I'm not really wanting to tell my parents. They'd be more than angry since I have an illegal app. I'm 14.

So how do I get rid of it As soon as possible?

Why can't i watch HD videos on my iPhone 5s?

I recently got this phone and moved into Verizon. When i went on youtube i tried watching videos on HD and it wouldnt let me. Is this a verizon network thing or is it the phone its self?