powers off after short time

I have a gen 4 photo 20 gig u2 iPod and a 30 gig 4th gen photo doing the same thing it will play music for about an hour or until song is requested to change they both have brand new batteries i have tried to start the gen 4 after the battery supposedly dies and it has a full battery i am starting to think it's the logic board. is there a way to know what needs repaired on them i also have a gen 5 that only last's 8 hours with a new battery is that also the same problems the 2 gen 4 i have also

yes i am from time to time i now have the same with a nano gen 4 16 gig