I have seen this issue with a defective top case before. One thing you can try is to get an external keyboard and mouse. Remove the bottom case of the computer, screws on the bottom of the unit. You can use the following guide here:
MacBook Pro 15" Unibody Mid 2010
There is a ribbon cable where the top case/keyboard connector plugs into the logic board. Disconnect that cable. to the left of that you will see a square chip. Right above the chip you will see two silver pads side by side. You can take a flat blade screwdriver and touch the end of the screwdriver with those two. Do not touch any of the other components with the screwdriver. The machine should power on. You will pluge in the external mouse and keyboard. Check and see if the machine shuts down correctly now.
661-5481 is the apple part number for the top case.
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