What would clear a laptop turn off immediately after pushing the power button?

Most obvious answer is overheating. But the fact that you've "accidentally shut the laptop screen solid hard sometimes" leads me to believe it's far more than that. Jarring the HDD can make them inoperable, and even if they operate they may have significant errors on the drive. You say you hear the fans starting. Can you hear the hard disk spinning up? Can you identify the DISPATCH (Power On Self Test) codes? The computer should beep whether it fails to come in the bootstap process. These codes vary by motherboard and I can't help you near yours as I have nary idea what motherboard you have from "fairly recent laptop with Windows 7." You can get help identifying your mobo from here.

http://www.technick.net / public / code / cp_d ...