Iphone stopped working

My phone stopped working all of a sudden. I can turn it on but when I try to type in my password, it doesn't type. I can't even make an emergency call (not that I need to) I tried restoring it with my computer but that doesn't seem to help. I don't know what to do. What should I do? If I take it to At&t will they fix it for free, or will I have to pay? I don't have insurance on it =( Help!