iphone 5s will not turn on only vibrates when plugged in

so about 6-8 days ago, I fell asleep listening to Spotify. The next morning, it was (understandably) dead. So I plugged it in and heard the charging ping, assumed it was charging and didn't look at it. So, an hour later I unplug it expecting it to have some power, but it stays black. I've tried everything; holding both buttons down (for minutes) plugging into iTunes, restarting, wiping it clean/ restoring it, and it still doesn't work. Help please?! I have an appointment at the device shop tomorrow, but want to try and fix it now. Now when I plug it in, it vibrates every 6 seconds. On iTunes all the stuff shows up and it says it's charging, and since I've restored it, there is a ton (11 GB) of free space. Please help?! April 2014 I got the 5S and then a year later I lost it, so I got a replacement this May. A month ago I cracked the screen gently and got it replaced. HELP ME!