I'm having the same issue with my N800. Out of the box, I charged it and it showed "fully charged." When I try to turn on w/ the power key nothing happens. I sent it to Nokia (thinking that it was a charging or hardware issue). They reflashed the OS (OS2007) and sent it back. It turned on once, then wouldn't turn on again.

If I plug it into the charger it springs to life. At this point I can press the power button.

I'm trying now to remove the SD card ( supplied card) and reboot a couple of times.