I did something foolish -- removed the battery without turning N810 off. When replacing the battery I can power up the N810 but before the process is complete the screen goes black and the system is powered off. Is there some combination of buttons that will do a cold restart to get the N810 running.
I've done that plenty of times when my N800 froze up. It shouldn't really affect anything other than lose your unsaved data and maybe make the next boot-up a bit slower. It definitely is supposed to just boot-up normally... Are you sure that the battery is charged up? You can charge without turning the tablet on.
The battery is a brand new Mugen which shows full charge measured by a meter. I tried the Nokia battery and it worked. Perhaps there's something about the quality of the connectors in the new battery. Thanks for your replies they helped me find the problem. I'll stick with Nokia batterries.
Battery length was the isssue. I used a piece of card stock to shim the Mugen battery and it worked. My thanks to the poster who recommended 3 layers of Scotch Tape.