Broken screen + won't turn on

Hello,

So, my phone felt yesterday and the screen got completely broken and even was out of my phone at some place.

When I put it on charge, the apple comes and go every 3 seconds.

I also tried to connect it to my computer, it recognised it for a few seconds and then the iphone icons in Itunes disappeared. An other thing is that the photo stream still worked as all my pictures synced on my computer through the cloud...

My question is: if i replace the screen would my phone work again? If not, what else can I do?

Thank you!