iPhone wont turn on but connects to iTunes after repair. Help!

Hello!

I recently bought an iPhone knowing it was broken. The description I was given was that the iPhone was dropped and the screen cracked, so it was repaired. However, now the iPhone will not fully turn on. It connects to iTunes fine, however, and when I told it to backup to the computer, the computer told me to respond to the iPhone.

I have several screens laying around so I tried one of them on the phone, and it failed to light up. I reset the phone and also updated and restored it in iTunes, however it still does not function. Interestingly enough when I plug in the phone is does not vibrate, nore if I switch the volume rocker. I can't nag this problem and I need any advice I can get. Thanks!