iPhone 3G keeps turning on by itself

So I`ve just bought a 3G to add to my ever growing iPhone collection. I`ve set the phone up and all is working normally however, when I turn the phone off it automatically boots straight back up again. My theory is possibly the battery, but I`ve noticed the screen has been replaced with a third party one, so not sure if that could be causing it. Any help would be much appreciated.

Luke