My Iphone 4s will not turn on? - 1

My Iphone for about a week would say that I have 1% left when really I would have 100% and last week it had shut off and now it won't turn back on. I got a new phone today but it says to save my contacts from my old phone I need to sync it to Itunes but since my phone won't turn on nothing pops up when I plug it in to the computer. Could someone help me try to save my contacts and photos please? Thank you!

Added (1). No I did not accidentally shut off my phone and no hitting the home or sleep button does not turn it on. My battery is completely dead and won't charge my phone is broken. I just need help figuring out how to sync it to itunes without turning it on thanks

You most likely shut your old one down. Hold down the start button (whatever you call it) for 2 seconds. See if that works.

And remember, somewhere in the world, there's a pug surfing, and ice-cream exists. Somewhere in the world, a kid is having the best day of their LIFE.
Also, you see my profile picture? That is a real live picture and that dog exists and so does that bird. Why don't you go throw a party and make memories? Or here's a cool idea: Take a video of yourself and talk about your life. When you grow older, you can watch it and see how much you've changed. Then you can show it to your grandchildren.
Take out everything inside a lip balm container and store money in it.
Take a bunch of printed out photos and rearrange them into a shape (heart, circle, act.) and stick them onto a blank and boring wall. You now have an awesome wall.
Go to pool. Fill up water balloons and throw them at little kids at the pool. That'll be fun for everybody.