When I tried to turn on my N800 after I'd finished charging it: it wouldn't turn on. What's the problem?

I would try to remove the battery and reinsert it after 10 seconds.
Does it turn on with the charger plugged in?

Was the battery dead before you charged it? Did you see the charging screen while charging?

yes and yes.

Try this:

1) Take the battery out.
2) Hold down the ON button.
3) Plug the charger in.
4) Before the screen shuts off, put the battery back in.

Your suggestion didn't work. Have you more?

The only thing I can think of is that it didn't charge correctly. If you have a volt meter, you can measure the battery. I'd also try charging from a different outlet.

I had this happen to my Apple iPod mini. I didn't use it for a couple of months and the battery went dead. I tried charging for days and every available troubleshooting method and came to the conclusion that the battery just died bcause it worked fine before then. I made up my mind not to buy any other Apple product where the battery is not user replacebale. My iPod mini is just sitting here as a brick (with original protective film on top!). The screen wouldn't even turn on with charger plugged in. It is DEAD!!

At least on the N800, you could easily replace the battery. If you are able to see the charging sceen when plugged in, your device seems fine. Like someone else said, try a voltmeter to check the battery voltage.

Do you normally "turn-off" (shut down) your N800 when putting on the charger? I don't. I am assuming that you know to hold the power button for a while to restart it after shutting down.If the voltmeter shows bad battery, you might have to order a new one (made by Nokia will probably cost you $50-60 such as this http://www.nokiausa.com/link?cid=EDITORIAL_184164) or an OEM knockoff will be much cheaper but probably will be of very poor quality.

If the battery is good, take out the SD cards and try again. Also, did you install any software between the last two shutdowns?

Where can one find a "voltmeter"

You can pick one up at Radio Shack, Sears Hardware store or Harbor Freight. You can usually get a cheap one for $10 or less, when you measure the battery you should have the setting on DC Volts.

Also there is something else you can try, but you have to do this at your own risk " I ASSUME NO RESPONSIBILTY IF THINGS GO WRONG".

What I have done in the past for rechargable battery packs that weere dead was take a 9v battery and connect a wire to the positive end and the Negative end of the 9v. Then the other side of the wires that are connected to the 9v battery touch the negative side wire to the negative side of the Nokia Battery Pack and touch the positive side of the 9v battery wire to the positive side of the Nokai Battery pack. Do this for about 30seconds to 1 minute and then put the battery pack in the Nokia and try charging it. It doesn't do it the first time try the sames steps again for a little bit longer, about 1-2 minutes.

What happens is the battery is so dead that the charging circuit will not charge it, the 9v battery will give it a little bit of a kickstart/charge and then it can be charged normally. Again this works most of the time but not all the time and I never had anything bad happen.

"AGAIN DO THIS AT YOUR OWN RISK"