iPod mini won't turn off and battery problem

My mini won't turn off sometimes and also the menu button won't work, like I can't go to the previous menu it just freezes or will only let me select stuff. So I can't turn it off and i press the play/pause button forever and the hold isn't on or anything like that. I reset it and it comes back and I can turn it off, but this happens a lot. Also my battery doesn't seem to be holding its charge anymore. It starts playing and then it tells me the you need to connect to power thing and then the low battery symbol and it turns off. Any help would be greatly appreciated, thanks!