Sounds like a bad power supply. One or more sections are shutting
down. Replace it before something gets permanently fried.

What I have just learned. While chatting on Skype, I clicked on
the video button (the one that starts and stops video transmission) and the
computer entered its dead mode. Amazingly, I can repeat this behavior! It
sometimes takes many clicks on that button, by the way.

I am thinking that the Skype software call to the video card (it is a NVIDIA
GeForce4 MX 440) is one heck of a clue. But, what is actually happening?
Is the card putting the processor into an endless cycle of interrupts? Is
the card jamming the bus?

By the way, the computer does not have to be running Skype to fail.

Thanks for your reply.