iPod question

I have a 6-year-old classic iPod which has been acting up lately. I knew the battery no longer held much of a charge (and I'm constantly re-charging the thing), but lately it's started cutting out mid-song, and showing only a blank screen. Does anyone know if this is an issue which a new battery (for $100 or so, I'm told) will fix, or whether I need to get a new machine? (For $250 or so - since I will have nothing to do with a Touch). It's a long and tedious drive to the nearest Apple store, so if anyone here knows the answer it will save me a half-day of lost work. (Best Buy for a new machine - if I have to go that route - is a LOT closer and more convenient).