You may want to look into water damage repair. This involves cleaning your logic board to rid it of any corrosion that will cause problems. You can remove the logic board with this guide:
iPhone 4 Logic Board Replacement
Once you remove the logic board, which is very easy if you stay calm and read the directions, then you will need to get a small, soft, brush. You will also need isopropyl with a 91% or higher alcohol content. You will need you soak the board in a small container of the isopropyl for about 2 minutes. You will then need to gently remove it from the solution. Look for any green or brown residue on the logic board and brush it VERY VERY gently. This is important because some components on the logic board are very fragile and can be broken of the logic board with a strong brush. Once you scrub the board down then place it back into the solution for another minute. Take the logic board out after this and place it on a flat surface and do not dry it off with a towel or paper towel. Alcohol will evaporate quickly. Let the board sit for about 8 hours and then insert it into your phone again. This will most likely get rid of any corrosion on the logic board which sounds like it could be shorting your power. If you don't want to do this yourself, then there is most likely a store around where you live that works with these phones. I have done this procedure on more than 70 phones and only about 10 of them still needed work after the bath. If you take your time and pay attention then it is hard to mess up. I would also get my hands on some disposable rubber gloves if I were you. It reduces the chance of oil on your hands causing other problems. Feel free to ask any more questions.
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