Some iTouch issues?

I recently got a broken iPod touch from a friend at work and am trying to fix it.

The major issue is the battery is pretty much shot so it works when plugged in but about 5min after its unplugged it dies. So thats an obvious fix, replace the battery. Problem is i have no clue what generation this iPod is nor does the person I got it from, anyone know a way to figure this out?

Second issue and more confusing the iTouch wont play music. When I pick a song it shows like its going to start playing the song but then doesnt and goes back to the title screen showing all the songs.

Ive tried goin in Pandora to play a song and it says that it is unable to play so there is something seriously wrong with the playback ability. Ive tried searching online for solutions but couldnt find anything.

Ive tried all the obvious things like restarting the iPod, and restoring it to factory defaults though iTunes.

Aside from the issues described above, the iPod works perfectly fine in every way.

Anyone got any ideas to solve my general ipod problems?