iPhone 4 dead, even after changing its battery

Hey I got and iphone 4 and it died a month ago , the problem was that it couldn't turn on unless plugged in wall or usb and when was in wall says connect to itunes when was on usb only the apple logo and turns off after 10 seconds it was on 5.0.1 and I changed the battery worked 1 day than died again even with a brand new battery on it and was charged but turned itself off, the next day it turned on when i connected to the pc and I did a restore to 5.1 it worked like fore 3-4 weeks and now dead again , I got another battery now and working , but I'm afraid that will die again ! I checked all water sensors and all are white , do you have any idea what it can be? thanks

iPhone 4, iOS 5.1