I had the same issues with my iphone 4s turing itself back on, only being able to turn it off while conected to my computer, sound issues and the diminished battery life. I tried hard resetting, wiping the phone, cleaning with brush, compressed air, etc.
Finally, I took my phone into the genius bar today. First I was told it had water damage becuase the indicators were red. However, after opening, they confirmed there was no water damage. Evidently this is a design flaw and there is a class action suit regarding it. He then told me the power up issue was a "board" issue. When I questioned him regarding numerous sites identifying bad dock connectors exhibiting these same issues he told me that it was untrue and that they did not replace dock connectors. I was told to either purchase a new phone for $200 (starting my contract with AT&T over again, no thanks!) or deal with it. I explained that for my work, I need to be able to power the phone completely off becuase it interferes with the signals at my work. (Him telling me I was wrong and having to explain to him that I've been doing my job for 30 years and knew what I was talking about, was a whole other issue!)
I next took my 4s to a cell phone repair shop. I told them what the "genius" said and what my research had shown. They told me it was either a battery issue or the dock connector issue, as I suspected. After taking it apart, it was confirmed to be the dock connector. I had the connector replaced and my iPhone 4s was good as new 30 minutes and $50 later.
If you are out of warrenty, have done your research and have tried all the simple fixes listed, please check out a reputable repair shop before purchasing a new iPhone or "dealing" with it.