iPhone 2G (2.2) not recharging - red battery showing

Hi all

I'm encountering the following problem:
My iPhone was nearly running out of power one evening, thus i plugged it into the wall charger. The next morning, I noticed that the iPhone was not recharged at all - it wasn't plugged in properly I guessed. I continued using my phone the next day, did a synchronization in the evening, everything worked as normal. BUT it stopped recharging and suddenly the red battery appeared as described in the manual on p. 33 right side (colored images). When I plug it in the charger, image on p. 33 left side appears.

http://manuals.info.apple.com/enUS/iPhone_UserGuide.pdf

So I guess, the phone notices when it is "on power". I let it on power for at least 10 hours, nothing changed! I did a reset (pressing power & home button for like 10 sec.) nothing, and iTunes doesn't recognize that there is a phone connected (as the phone does not boot).

I put the iPhone in DFU-Mode and iTunes recognized it and i was able to do a full recover without any problems. But at the end of the recovering process, it went back to the red battery...

Any ideas?

I guess, that there is a broken controller measuring the battery power or anything like this...

would it be an idea changing the battery? I didn't notice any big decreasing in battery power...

Thank you for any help!
Kind regards