Hi I may have just got lucky with mine. I would do what the other guys suggested, take it apart piece by piece and look over all the components (with magnifying glass if you have), make sure none of the tiny components are missing or any of the connections have small breaks in them. Put it back together carefully making sure every connection clip is down hard in place (they can easily come loose).
When plugging into a computer is the iPhone showing up in iTunes? if it isn't it could mean a problem with the motherboard or there could be software issues.
For me changing the battery and screen for new one's fixed the problems, but this may not be the case for everyone. It could be other things like the dock connector that needs replacing if things aren't charging / syncing with computer properly.
I also tried making every component to work (front/back cameras, vibration, speaker, microphone, wifi, bluetooth, headphone jack, volume buttons etc) just to see that they are all working and weren't contributing to the problem. If one of those aren't working it could be contributing to the phone not working properly and would need replacing.