Interesting philosophical question: Is a tower PC that's not plugged into anything (neither power nor a keyboard or monitor) a computer? Does computation happen if nobody can perceive it? And is a computer a computer even between two CPU cycles?

> no independent IO

I would challenge that! How is a smartcard different from a server in a qualitative sense? Both get all their I/O over the network.

Some cards even have a display, fingerprint reader, or can blink an LED (the latter unfortunately only indiscriminately when powered up, not in response to any computation, I'm afraid).

I've never heard a definition of a computer to include its power source.

IO is of course required.