Flashing Apple logo when plugged in

I own an iphone 4, and recently my iphone stopped working completely, no feedback at all. When I plugged it in, it woudln't come up on iTunes, it would only flash up with the apple logo as if it's booting up, then shut off after about 5 seconds, then come up with the logo again etc. I've also noticed that when I plugged it into a dock, the apple logo would not dissapear but instead stay, after a little while, it would do the double vibrate to show it's charging before shutting off about 10 seconds later. I've tried many button variations such as DFU mode, holding home button while connecting via usb, I don't know what else I can try, please give any suggestions!