My iphone won't turn on at all?

I turned it off because it was being stupid since the memory is pretty full. I tried turning it back on and it comes up to the white screen and apple logo for a few seconds then stops and the screen goes back to black. I've tried pressing the sleep button and home button and it just goes back to black. When I plug it into my computer it doesn't recognize my phone is plugged in. I have my phone plugged in right now. I can't reset it because it won't let me and plus I have the beginning of a college essay saved on it. Can anyone help me out? Or should I just take it to verizon?

What was happening to it before that made it "stupid"? The memory being full shouldn't affect it at all.

let it charge overnight, then try turning it on, and if it still won't, take it to verizon or an Apple store nearby, be expected to have to pay for a fee to repair it