Iphone 4 turns off and on unexpectedly

So i have an iPhone 4 CD MA it is on 5.1.1 and is 8gb. I dropped something that never happens and it acted like a slinky and continued to roll down 4 stairs. At first it was just black wouldn't turn on at all, it was mostly charged maybe 85%. I put it on my dock and the apple logo came on, but my iPhone wouldn't boot up. I took it off the dock and the apple logo disappeared. I tried putting it into or off of sleep mode just in case and nothing happened. I plugged it into my laptop with a cord i know works and the apple logo wouldn't come on and iTunes wouldn't recognize it, nor would my computer. So i put it back on the dock to see if the apple logo was just a fluke. It came back onto the logo and i tried sleep mode, DFU mode, and just plain holding the power button. Nothing happened except the apple logo disappeared and then came back later. So i left it on the dock to research and it booted up, took it off the dock and it went black again, put it back on the apple logo came back and it rebooted up. So i checked to charge to see if that was the problem but it said it was fully charged so i tried it again, off the dock equals off. After it was sitting on the dock and booted up I just tried it plugged into my computer again and nothing, not the beeps my computer (or the iPhone I'm not sure) sends out, not the charging green battery on the phone, iTunes didn't pop up, nothing.

You have better to send your iphone to one of those authorized businesses to fix~