Very Strange Ipod Nano 1st Gen behavior...

Question

I've had my Ipod Nano for quite a while now, and it has served me faithfully, without problems until only a few days ago. Suddenly, and without apparent cause, it ceased to activate via the select button. I attempted the reset trick, without success.
My first instinct was that this might be a battery issue. I plugged the device in to charge overnight, and the next morning tried activating it, with the same results: Nothing.
I noticed that, when I plugged it in to charge, the Ipod did not activate and go into the "do not disconnect" screen as normal. In fact, it did nothing. Feeling experimental, I tried plugging it in and pressing the select button. Nothing. While plugged in, I tried the reset trick. Success. The Ipod booted, taking slightly longer than usual to get past the Apple logo screen. After a few seconds longer, it went into the charging screen. I left it overnight again, and checked on it the next morning.
Now the screen showed "Charged." Suspicious that this was still a battery issue, I loaded up a few hours of music and checked on the unit repeatedly over the course of the day. It definitely made it past the 8 hour mark (playing mostly 128kbps at a low volume), but I can't say when it finally quit. The battery seemed to perform normally. I charged it again. Here's where things get strange.
Currently, the Ipod will only activate via the reset trick, and only when connected to a power source. It will remain activated for several hours after being disconnected, and seems to behave normally while activated. Once deactivated, the unit will not reactivate unless connected again to a power source, and again, only using the reset trick.
The battery charges, but only when the unit is activated. If the unit is deactivated while connected to a power source, it will not charge.
This almost certainly cannot be a battery issue, as the unit still plays music, and lasts 8 or more hours after being disconnected. The boot time seems to be affected as well, as it stays on the Apple logo for much longer than usual (up to 15 seconds) before showing the "do not disconnect" screen. I've updated the unit, formatted it, and restored it repeatedly, and yet it still will not activate when not connected to a power source.
Any suggestions (other than "Change the battery" as this almost certainly cannot be the problem)? Otherwise, this unit will simply be destroyed and disposed of. I have no sentimental attachment to it, and it doesn't make sense to pay it's purchase price again to have it repaired.

Answer 1

Yes, I did try restoring it. Multiple times. That didn't help.
I noticed today that the casing seemed warmer than usual after a charge. I saw this article:
http://news.cnet.com/8301-135793-10020108-37.html?hhTest=1&part=rss&subj=news&tag=2547-13-0-20
So I'll take the thing by the nearest Apple store and see if they'll honor the replacement suggestion.