Disk Utility reports a fatal Hardware error.

Hi! From what you mention, it sounds as if the hard drive is failing. If you have data on the drive, it would be a good idea to back it up now so that if the drive crashes permanently, you won't lose data. If the drive is still working, and you do not keep valuable data on the Mini, you could always keep using it until it dies. I use mine, for instance, exclusively for video streaming, so if my HD got an error, I'd probably just let it go until it blew up and then deal with it. :-)

If you do choose to replace the hard drive, this would be a good opportunity to install a larger one, and possibly upgrade the RAM as well, depending on how much is in there.

Here's iFixit's PPC Mini hard drive replacement guide, which sounds like it's probably the one you need:

Mac mini (PowerPC) Hard Drive Replacement

There are also some good video guides on YouTube that walk you through the process, and that is helpful because there are steps to the Mini process in particular that video can make clearer. Does anyone know whether this older Mini uses a SATA or PATA drive? My Mini is an Intel and uses SATA, but this one is PPC and I suspect PATA.

I'm unclear as to what you mean by replacing the battery, since this is not a laptop and does not have a battery, unless you're possibly referring to the PRAM battery?