I've ran into a spot of trouble with my 80GB iPod Video recently. The TL;DR: I think the logic board on my iPod has gone faulty, but I don't really know enough about the hardware to know if this is actually the problem or not.
I didn't notice any precursor trouble before one day, after falling asleep listening to my iPod with a sleep timer on like I do most nights, my iPod wouldn't turn on. It appeared that the battery had gotten too low for it to provide enough power to boot. But even when I connected it to external power (both wall outlet and computer), it couldn't completely turn on. I would see a quick flash of the battery icon with a caution sign, then the Apple logo would appear for about a half second before turning off and repeat the cycle, stuck in an endless booting loop. Since it still had the original battery, I figured that the battery had died overnight and I would need to replace it.
When the correct battery arrived (I originally received the wrong battery from a random seller on Amazon, my second battery came from http://www.ifixit.com/iPod-Parts/iPod-Video-60-80-GB-Replacement-Battery/IF195-028) and I installed it, it seemed to work beautifully, and I initially thought everything was good. However, when I disconnected it from external power, I noticed that the battery was stuck reporting itself as "charged". Rockbox still gave me a "percent remaining", but the battery still reported that it was charged. I didn't investigate too much with the Apple firmware, but I noted that the battery icon was fully charged persistently there, too. Resetting the iPod didn't change this issue, so I tried to run the battery out of power and see if that would fix it. After this, the iPod got stuck in that low power boot cycle.
At this point, I did figure out how to charge the battery. By disconnecting the hard drive and putting it into diagnostic mode (hold rewind and centre while booting), I was able to get the battery to charge, and charged both my new and original batteries. It seems that both batteries are totally functional, but the iPod thinks the batteries are charged whether or not power is connected.
I should note here that in Rockbox, everything seemed to be working completely normally except for the battery being stuck "charged". With the Apple firmware, things were crazy slow and laggy, but I've read that this is due to the way it draws and discharges power to allow the iPod to remain connected to power indefinitely without overloading the battery. When it thinks it's constantly connected to power and can't disconnect, it gets stuck in some sort of infinite loop and bogs everything down. The most important way that this impacts usage is that because it always thinks that it is connected to power, I cannot turn the iPod off. I also suspect that it interferes with the iPod powering down at the critical point before the battery gets too low, so the discharging battery totally drains and does not keep enough power to boot.
I then tried to do a full restore with iTunes, but to no avail. The battery is still being reported as "charged whether or not it's connected to power. My best explanation so far is that it's a hardware issue, as the full restore would have resolved any firmware issues. I think that whatever component that reads the battery status (charging, discharging, or charged) has broken, and I need to replace this part. I'm really not familiar with my iPod's innards, but my best guess is that I need to replace the logic board. Is this an accurate conclusion, or what else could be the problem?
Thank you for your time reading this and helping me!