hp ipod problems

so i bought an ipod from craigslist and this is weird ok but here we go! I started having problems with the charging so i replaced the battery then i still had problems with it but when i called apple support they said that the serial number was invalid and they couldn't look up the info i get the same number when i look at the menu as when i do when i look at the back and then i can't get it to sync up to my pc either so if anybody has any kind of info about my problem and what to do please help me out because i am going insane trying to figure this one out! Oh and my pc doesn't even recognize my ipod and i have done everything imaginable to make it sync!