Thought it better to repost here....
Thanks to all ... The many contributions helped me.... My Toshiba P55W-C5200X had the same problem immediately after changing power options from "open lid = power on" to "Power switch = power on". Opened up the back to try the various fixes recommended however I found power switch had fallen apart. (So much apart that the "Push down on keyboard just above power switch " could not work for me. I removed the switch (3 pieces), then bridged the switch contacts. Laptop powered up immediately. Next I went into Power Options and set "When i press the power button:" to "Do nothing" AND "When I close the lid:" to "Sleep " for BOTH "On battery " and "Plugged in". Saved changes then clicked "Panel Open - Power On "... Toshiba System settings window opens... Scrolled down to find "switch" and Enabled "Panel Open - Power On ". ..... THEN I replaced the base.