It took some time to get the case apart, but it finally got done. My wife and I worked on it. She is 1000x more patient than I am. The blue tools were worthless. We found a YouTube video where they were using atomic bombs (kidding - it was other tools) and we were finally able to get into the iPod Classic. The instructions on this website were good. Battery seems to be working fine. This makes me despise Apple even more though. I don't like how hard they make it to repair items yourself. I'm not much of a do-it yourselfer, but I try. I did change out a hard drive on a desktop before and that went fairly well.
I'm glad I found this website - I was starting to mourn the impending loss of my iPod Classic 160GB as I have a lot of music (almost 60 GB) on it. Anyway, time will tell, but so far the battery is working great!