I had many of the symptoms in this thread (dead n800 after running down battery to zero - unable to restart, occasional charging icon and/or NOKIA screen but boot never progressed beyond that)

Tried many of the suggestions but to no avail - including the fridge

I figured the battery was SO flat that the n800 might have some flawed logic in it that would not allow the battery to charge so I pulled the battery and wired it directly (using speaker wire and sellotape - not pretty!) to a spare Nokia ACP-12X charger that I had lying around. I wired it as inside + outer -.

30 mins later, when I put it back in the n800 it booted first time. It is now up and running and charging happily. If there is such a thing as an external battery charger then I am buying one tomorrow!

Meanwhile I may look at a reflash as bunanson, in post #100, seems to think 2007.51-3 has a beneficial effect