Sony DSC-W5 Cybershot won't Power Up!

I have replaced the batteries, but no go on Power. I took the new batteries out and held down on the power button for fifteen seconds. Then I replaced the batteries and still there was no power. I read somewhere that there is a "dummy battery" inside the camera. Could this be the culprit? Should I replace that "dummy battery"? Obviously, being that I have no A/C input on the camera, I figured there must be another battery inside the body of the camera. What could be wrong with this camera? It is only one year and six months old. I am gentle with this camera and never abused it. Afterall, it cost me $348.

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