iPhone 4 wouldn't turn on; went into restore loop, now won't turn on again

My iPhone 4 wouldn't turn on for the past few days despite it being fully charged/plugged into laptop when trying to turn it on. Tried all modes of restoring in yesterday, to which none worked. Tried entering DFU mode one last time and, to my surprise, it worked... or so I thought. After trying to restore it via iTunes back-up, it just went fine on iTunes, but went back to the set up screen (http://www.iphoneproguide.com/wp-content/uploads/2013/09/Hello_270x405.png) after you enter DFU. I then tried restore as a new iPhone and it went back to the same setup screen. Left it for a little bit, came back and now it won't turn on again. Any ideas on potential fixes?