I thought I had killed my brand new Raspberry Pi 2, which was showing just a steady power light and that was it -- just like the state the machine is in after typing $ sudo poweroff and before disconnecting the power pack. The mouse sensor was unlit, and the CAPS LOCK and num lock lights on the keyboard were dead.
However, it turned out to be a false alarm.
I disconnected the Internet, HDMI, keyboard and mouse cables, leaving only the GPIO connections (which there were a lot of, and I really did not fancy disconnecting them unnecessarily). Then, on a whim, I decided to try powering it up again -- and this time, I noticed the "disk" activity light flashing, and the lights on the Internet socket also flashed briefly.
Encouraged by this, I tried reconnecting just the keyboard, and noticed the caps lock and num lock lights were working. So I tried logging in blind (it's not all that difficult, actually; remember that ctrl+U erases everything you typed since the last time you pressed Return, so you don't even have to remember how many times you need to press backspace) and running my little test program.
And it worked!
So I shut it down cleanly; reconnected the mouse, Internet and TV; and powered it again. And was back in business, just in time for Pi Day (22/7)!
Thinking about it, the problem must have been caused by the TV, network switch or (less believably, because they don't have any external power supply) the keyboard or mouse applying out-of-range voltages to pins and latching up the Pi's processor.
Anyway, the moral of the story is: Some faults are recoverable. Try disconnecting everything before you condemn anything.