Apple I-Pod 4th Generation Battery

My silver I-Pod Nano 4th generation is not able to power on. It works fine when it is connected to my speaker or charging cable but not alone even after charging for a long time. It plays music in the speaker fine and everything else is functioning, just not when connected to a power supply. I think it has some thing to do with the connections to battery because when it is not being charged, nothing turns on. (The power Switch on the top is on the power mode (not orange)) If someone could help me pinpoint the problem so I could see if it is fixable. Thanks

-Nick