How to unlock Iphone after it says Connect To Itunes without restoring?

I accidentally forgot my password to my iphone, i just changed the password a few days ago. I want to have my iphone back, but i don't want to lose all of my data.(I have lots) i've looked online that you must be connected to the same computer as when you first synced your device, but i don't have access to that computer anymore. When i tried to connect my phone to itunes on my laptop that i'm using right now, it said, " can't allow access to iphone -- must be unlocked" the problem is, i can't unlock it because its telling me to connect to itunes to fix it --- I'm so confused and angry please help me here

How to Retrieve a video i Deleted on my iphone 4S?

Today i deleted a video off my iPhone 4S forgetting that i wanted to put it on YouTube. Also, i don't know if this helps at all, but from my phone, once i made the video i put it up on my Facebook and it's still there. If i can't get it back on my iPhone can i somehow get the video from Facebook and save it to my Computer?

I had tried one program called: Wondershare Dr. Fone, it was apparently free, but then i downloaded and waited for like an hour while it loaded my phone then asked me to buy it. F'in stupid false ad.
Anywho, any help will be appreciated, thanks!

Added (1). I have never set up my icloud

Added (2). Your link worked, thanks man. I'd pick best answer now if i could

IPhone 5 walking dead game

So I got the walking dead game on my iPhone 5 I downloaded the 5 episode pack but it didn't show the amount downloaded and I checked to see if it was available it says coming soon, how do I see the amount downloaded and do I need to connecting to Wi-Fi?

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How to transfer sms from Windows Mobile to Iphone?

I've been using my windows mobile over four years and there are lots of memories through sms

2 days ago I shifted to IPHONE but now I badly miss all the sms from my old phone. Can anyone advise me on how to import them.

I need sms like normal sms/contacts in phone. Can you help me with it?

Why does iTunes keep deleting my playlist?

Most of the playlists on my iphone i made on my phone (rather than in itunes) so they don't show up in itunes when i plug my phone in, it only shows the ones i made in itunes. The problem is every time i add music to my phone it deletes all the playlists that aren't in my itunes library. Many people have said that the way you fix this is to "manually manage music and videos" however i already have that checked (i always have since i got my phone). Does anyone know what could be causing this problem?
Another peculiar thing is whenever i modify my phone at all (add/delete a song/video/audiobook… Etc, or even just rename something) after i click ok, in the top screen/window/box (where it tells you what it is doing) it says: "syncing >song name<" and x of x (eg: 1 of 256) and a progress bar. There's usually about 200 some songs it goes through in 10-20 seconds. The funny part is i have way more than 200 some songs on my phone and the ones it syncs don't seem to have any relation to each other i.e. They aren't all on one playlist or they weren't all just added, they aren't all from the same artist, they don't really have anything in common. I believe it is the same few songs every time. I don't understand why whatever it is doing it doesn't do to all the songs and why it does it every time even if i don't do anything to those songs. The first time it happened it was with 8 songs (the same ones every time), then it moved up to 40 or 50, then 100 some and now 200 some. It kind of worries me. Can anyone help?