Classic iPod Charging Problem

I wonder as to if someone could guide me to cure the peculiar problem that I have, as follow, on one of my Classic iPods which is 6the Generation 160GB (Original Model, not the Latest Model). It does not show the Battery Charge Status Icon during charging, and the screen just goes to dark blank. I can still use the iPod, however, since the battery will be somehow charged up. It is a slow rate charge and takes 10 hours or so, but it will be fully charged. I then can play my music for nearly 20 hours, so that the battery itself should not be blamed for the "Charge Status Icon No Show" and "Slow Charge". Since the large Status Icon does not work during charging, I must push the Center Disc Switch or the Menu Switch to wake up the screen and go by the Small Battery Icon located at the upper right corner in order to see as to how much has been charged up. Let's say that I have started charging 5 hours ago when the Small Battery Icon has indicated, with green color, 20% or so of remained battery energy. It is quite disappointed though to see this 20% or so of green area once again 5 later. I felt when I saw this "20% Green" as the first time that there is no charging at all in 5 hours. I felt that this iPod does not take charge any more. I was wrong, and it has been charged, however, and the peculiar fact is this. When I push the Center Disc or Menu Button at this 5 hours of charge point, the green area of the Battery Icon suddenly changes from 20% to 60% as the screan chages to the next menu items. I was so disappointed a second ago to see this same 20% green, but I am now very happy to see 60% green. 40% has been charged in 5 hours. If I continue for 5 more hours of charging, the green area will increase to 100% of full charge point. It took me a several days of experiments to find that the charging circuitry is still working, although its function is not perfect. It took me a quite some time since there is no quick charging and it is a slow rate of charging, in addition to the fact that the Small Battery Icon does not indicate the charge status value in green immediately and there is a jump indication involved. Now for the cure, I have tried to restore the iPod with the iTunes twice although I felt that the problem does not lie within iTunes or within computer. I believe in this way since 4 other iPods that I sync with the same computer do not have the same Battery Charge Status Icon problem. I have also tried "Push and Hold the Center Disc Switch and Menu Switsh at the same until the Apple Icon comes up" kind of re-setting operation 3 times, but none of my attempts has solved the problem. Please help. I apologize you for my long writing.