Interesting, the same thing that happened to the original poster happened to my H320 (de facto a "H330") yesterday, including
* the way the buttons didn't work (no Stop, Right was Down etc)
* that the behavior went away after taking the thing (partly) apart - and that it returned the next day
* strange battery indicator similiar to what was desrcibed by dYna - had it on the power adapter the whole night and it would show 6% - or some high value like 80% after a hard reset (only way to turn the thing off without a Stop button)
* I remember getting the message about the "etxernal battery pack" once, too
A few hours ago I disassembled the thing more or less completely and also disconnected the battery (had to set the time/date again in Rockbox afterwards).
So far it works and the battery indicator is showing 95% .
It will be interesting to see what happens tomorrow or after recharging it the next time.
And some random thoughts:
I wonder if the stronger 2200mAh of unknown-ebay-origins replacement battery of could have something to do with this?
I had been thinking about replacing it in a couple of months because it had developed the same behavior the original one showed during its last months until I finally had to replace it:
after booting the battery indicator would show something like 45% and then slowly climb up another 20% or so over the next couple of minutes; for example, the "95%" mentioned above were only "86%" right after the start.
Could a dying battery mess things up that way?
Or maybe it could be an insulation issue?
I accidentally dropped the player *very* hard 2-3 times during the last few days so something might have slightly moved inside and my H320 has been a bit iffy insulation-wise in the past (at least after replacing hard drive and battery; I don't remember, but I think the 2200-battery might have been slightly thicker than the original one):
* yesterday I started unscrewing the case once while the player was still running and I could actually hear a humming sound in the earphones when the 100%-metal screwdriver touched the screws (ear-phones were connected to the Line-Out jack; the earphone jack produces some low noise that is noticeable with the low volume I use when listening-until-I-fall-asleep).
* after replacing the battery (IIRC) I could always feel current in the silverish frame around the buttons when the player was on the charger (I had to put insulation tape over the buttons to not get mildly zapped each time - I was too lazy to (dis)assemble everything again

)
* when using very low volume, I could tell if the player was plugged in or if it was running on battery because in the first case there would be a noticeable humming sound in the earphones