I also have this problem with my n810 purchased around 04/12/2007 at buy.com. It powered up normally for the first time. I did not charge it before turning it on but the indicator showed a decent charge level. I used it for about 20 minutes without the wifi before I pluged it in then it charged normally. The batteries should be OK as the device lives up to the specs wrt the operation times. I didn't switch off the device for at least a week, at least I don't think I did. Then after at the end of a charge cycle when I removed the cable it shut down and I figured I had this problem .

None of the tricks listed here work, like removing the batteries or waiting for at least three minutes before trying to turn it on. The only way I can turn this thing on is putting it on the charger and waiting until it thinks so.

Today I tried a non-official charger, an nokia acp-12e from an older device, that provides less current than the AC-4U that came with the device (800mA vs 890mA) and it seems that now it takes more time until the charge sign appears. I also suspect that it takes more time if the battery is more discharged. From this I would think that the device falsely sees as if the battery was discharged too much.

However I found a bug that might be related #2290. This is also describes a case when the power button doesn't work properly. If you configure your device to go to soft poweroff when duple pressing the power button then it won't come back from a duble press. It's only able to wake up by a long press (if you configure so, of course). This might or might not be related.

Anyway it's an interesting option for those who don't send the device back (yet): configure your tablet to go to soft-off on a long press. It will come back instantly (<1 sec) on the next long press and it will prevent you from turning off accidentally and still you'll be able to save some power. (I haven't looked it up but I guess this soft-off mode is like suspend on desktops and laptops. The CPU is shut down but the memory stays powered.)