iPod 120GB Classic Gen 6 won't keep a charge

I recently replaced the battery in my 3 year old Classic. It seems to charge fine and perform well, but after about 2 hours the battery life indicator is in the red. I've had a second battery installed, done a soft reset, and finally a Restore. Same problem--charges fully, then seems to really suck battery life. If I charge it and leave it overnight, it is totally dead--not even an Apple screen. I don't hear any hard drive clicking or notice long access times--in other words, it seems to work fine, only now with a 2 hour life.

Since a second battery is in the unit, I'm guessing the problem lies somewhere else. Maybe the logic board, or the hard drive itself?

Has anyone experienced this problem and found a solution? I really like the size and capacity, and I'd hate to have to dump it.

Thanks in advance!!