The power button board is bad. That is a small, PC board behind the power button that connects to the motherboard. I have had to replace several of these. They are small, surface-mount boards with three wires on them that come loose with the slightest tug. Unfortunately, on my Studio 1558, the power button is up by the right hinge, which when opened and closed, flexes the wire for the power button board. You have to remove the top portion of the laptop (the palm rest bezel, the keyboard/speaker bezel, and keyboard itself) along with the screen bezel. Then you have to loosen the hinge screws on the right to have the hinge move freely, so you can get to the power button board. One screw holds it in place plus a tab that goes into a plastic slot on the power button frame itself. Once you undo that, follow the cable and unhook it from the board. I got a new power button board from an eBay seller for under $10.00 and installed it. When installing, hook the power button board back in behind the power button, secure with the tab and screw, attach the connector to the motherboard and start routing the wire from the connector forward to hinge. Make sure there is plenty of slack in the wire up at the hinge so it has room to move without disconnecting the 3 small wires on it. Once they disconnect, you cannot reconnect them unless you do surface-mount work. Then put the hinge back together, replace the bezels, and you are done. Your power button should start working again.