My iPhone keeps dying.

Since a few days my iPhone 4 cdma just all of the sudden turns off and won't turn on until you plug it in to a charger. It boots immediately and is at the percentage when ever it turned off which is often like 90 percent. Holding the home and power button also doesn't work. I already tried replacing the battery. Another way is to unplug the battery and plug it back in then it will boot without having to charge it. I really don't know how this could be. No water damage by the way.