iphone 4 keeps shutting off

Ok. just received a new Iphone 4 to replace my old Iphone 4 as it had a hardware error with the virbrate. I have the new itunes and new OS.. all backed up. I have had the phone for almost two weeks. I was played like 3 songs and it just turned off on its own and the touch screen stopped working. It took me a while to get it back powered on. I just had it power over using the flashligh app.It would not turn on. I waited 20 mins and got it back. Is this a hardware problem with the replacement phone or is it a problem with the new OS 5? What can I try before making another hr drive to the apple store?

thanks