How to get old info off Computer?

This may be long and confusing, I will try my best to explain:

So basically, I need some data from my old iPhone which is synced to iTunes on my old computer. But the new iPhone I have now has the new ios 7 update and is too new to be synced with my old itunes, I can't download the new itunes because the administer forgot their password and I can't downgrade my iphone to make it sync-able with my old iTunes… These files are very important to me… Please help.

More thorough:

SO I gave my old laptop to my mom to use, then she gave it back years later ( now ). My old account was still on their, all my old files, pics etc.

I got an iPhone 4s and synced it with that lap top before it had the new ios 7 update. Instead of restoring as a new iPhone it restored to my old iPhone i had years earlier.So, all my old pics, notes, contacts, etc that were on my old iphone got put on my new iPhone. I was very happy because a lot of old notes i thought I lost were put back onto my iPhone. THEN I plugged my iPhone on my friends computer, got the ios 7 update and after doing that I lost all my old notes off my phone. So I thought i could plug my iPhone into my old computer again and just restore it again but I can't do that because the iTunes on my old computer is ' too old '… I need to download the new version of iTunes.

In order for me to download the new iTunes I need to put in the administrators password, which is my mom and she doesn't remember her password

OK, OKAY, CALM DOWN.

Here, download this software, no installation>>>https://www.thinkskysoft.com/
It is called itools. Should do better than itunes does. However, you must know the directory of the old files on your old pc.

Iphone 5S Giveaway

Free.

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