Why is my iPod Mini shuts off when disconnecting my cable?

Hello. Since I got an iPod Mini 2nd Gen (6GB) from eBay with 2 new batteries (both are tested) and it completely shuts off when disconnecting the cable. When I say that both batteries were tested, I mean that I switched the battery from iPod Classic 4th Gen (Monochrome) to a battery that is new from the iPod Mini and the extra as well. For a while charging the battery with the iPod Classic and plugging it back to the iPod Mini, it does turn on but it doesn’t want to charge with the new battery. When I’m not charging with the cable, it said that the battery is charged, even though it’s not connected with the cable & a power source. But when using both of the batteries to an iPod Classic, the battery does charge & doesn’t say that it’s already charged when it’s not plugged to a power source, it tells me how much battery has left & it doesn’t said that on my iPod Mini, only said “Charged” even though it’s not plugged in. Does anybody have this problem? If so or has answers, what does it mean & while I’m trying to fix it, what is the possibility to fix it? I’ll comment more questions when I’m on new problems or needed more help. -iPod Mini user