Ipod Nano 4th generation troubleshooting

I have an ipod nano 4th gen and it's about 5-6 years old. It's been acting weird for about a year now. The battery bounces around, not just draining and not over hours or days but minutes. It goes from fully charged to low back to 75% to needing to be charged. And again, that's in minutes. This was the main problem until 6 months ago. Then it began shutting off and giving the apple logo. When I'd turn it back on (holding down either the play and center button or the play and menu button) it would need to be charged. Due to this for the last 6 months it had been dead when I charge it (don't know if that makes a difference) but the same battery issue happened. Now however, it's stuck in a loop. I charged it for a road trip and noticed the computer didn't recognize it (by computer I mean iTunes) It would go from the apple logo to the menu (showing a battery fully drained but not charging like it should've) then to the triangle saying it needs to recharge. Then it would start all over by going to the apple logo in an endless loop unless turned off. I've reset it but nothing changed. I tried just leaving it in to charge both in a computer and car charger but nothing happened. Help please! I'm a cheapo and would prefer not to spend a ton of money fixing it or buying something new!