How do I diagnose which component is bad.

I was given this iphone 4 after the owner had recently taken it in to have the screen replaced. She said it worked for a day and then nothing. The repair man did not stand behind his work. when I plug it in to charge it a white apple lights up then disappears and continues to do so. I've taken it apart and checked all connections and check the battery at the connecter and its putting out 2.8 volts. I tried DFU mode but had no luck and since I'm not the original owner and it's been worked on already I can't fall back on the warranty. I don't know what to check next.