I did some searching and found that with some of the Sony Cybershot's the type of battery also makes a difference. Most sites I read specifically made mention to the cause being a difference between the type of batteries (e.g. Alkaline vs Lead). The common fix was making sure you were using Alkaline batteries. However, this was from searching for just when it was turning off very shortly after turning the camera on so I'm not sure if that will be useful to you as well in the current state you are in.