Laptop that only boots after being placed in the freezer once all power is depleted?

I have seen this before in some laptops.

Take the battery out. The laptop should run without the battery in place (with the adapter plugged-in obviously). Then, when your session is complete, shut down. Reinstall the battery and charge as normal.

I had the exact opposite problem with a customer's Vaio laptop..it wouldn't boot unless the unit was warmed, typically in an oven for a few minutes until it was warm to the touch. I took it apart, heated the motherboard in the oven, then powered up the board..and hit various regulator components on the board with freezer spray while the board was running..sprayed one of the caps and the board died. Solution? Replaced the board, since the individual components are not marked and no specs are published. My suggestion is to use freezer spray on your motherboard and see if the board comes alive. At least this verifies that you have a bad board.