Hard repeated crashes

Someone please suggest a possible fix. I bought this iphone off of craiglist and it was working perfectly fine. The phone is in clean condition, no scratches on the screen or the back. Just a hairline crack by where you plug the charger. I came home and unlocked it and jailbreaked it using blackrain and it was working fine. right after the first call i set it down and it turned off. I pressed the powr button and it restarted (i knew something was fishy but i did not wanna think that way). It continued working for another few hours and then completely shut down. I connected it to the itunes and it wanted to restore the phone and said that it was in dfu mode. When i tried restoring it got stuck half way through. After a few times it did restore only to shut off again randomly and back in the restore mode. The restoring gets stuck at random points or the phone doesnt start at all. But when it is restored everything works perfect, until it shuts down.
I have resored the phone, restored it in dfu mode, home+power button, hard reset. Nothing seems to have had worked.
I am also a brand new iphone user, got my iphone for 2 weeks (not this one, this was for my friend). But i have read everything available and have tried most of it.
Please Please please help, paid $330 for this damn thing and it doesnt work.