I am having reboots every five seconds or so after switching my N800 on this morning.

Interestingly, it keeps rebooting if it's plugged into power. If it's on battery, it lights up with the Nokia sign, waits five seconds, then turns off.

So I wonder if the problem is power-related. Perhaps a bad battery, something like that. I notice the device won't power on without the battery installed, although plugged into power, so perhaps the battery isn't charging, something like that.

I'm having the exactly same problem and symptoms.

Interestingly flashing the firmware still works but does not fix anything.
I have also removed all my SD cards to no avail.

Background:
During the night n800 had run out of battery. I tried booting it with the power button but it just flashed the blue led. When I plugged the power in it launched a screen with battery loading logo in the middle. After waiting around 10 seconds I pressed the power button again to try if I could get it to boot with the power plugged in. It tried to reboot, but went into the infinite reboot hell.

The only state where the N800 won't keep rebooting is if I leave the power plugged in after flashing. I'm going to leave it like that now for 30min and hope that it might recharge a bit.

I was able to recover by flashing in R&D mode (mentioned elsewhere here).

I might have made some progress:

After flashing with the following command I managed to get into a recharging screen that does not reboot immediately away.

flasher -F RX-34_2007SE_2.2006.51-6_PR_COMBINED_MR0_ARM.bin -f -R --enable-rd-mode --set-rd-flags=no-lifeguard-reset

After letting the n800 recharge for 30 minutes I got it to boot normally and restored my backups.