Hi Loren,
Glad you're back up. That pesky battery has perplexed plenty of people, especially when it's tested and shows "good." I've had batteries that kept a Beige from booting work fine in older Macs. They tested 3.2V "in-hand"--supposedly an indication the battery is still within spec. Still, not good enough for the Beige G3.
Now that you have a new battery, there are ways to maximize its life. The main step is to leave the computer on wall power at all times. That way, a 5V trickle current bypassed the power supply and keeps the PRAM powered, along with the ADB bus. If you routinely unplug the computer or use a power strip, power center, or backup power supply to cut power to the computer, the battery has do all the work to retain PRAM values and its life can shorten to months.
As long as the computer stays plugged in, it should last three years. At that point, I install a new one as preventative maintenance.
If you need to store the computer or have it off wall power even for a few days, take the battery out and tape it to the outside of the case. Never put the computer in long-term storage with the battery in place. One poster in the pre-G3 forums removed a Mac from storage and found it dead. When he lifted the hood, he found that the battery have leaked and corroded the copper off the logic board. The computer was DRT ("dead right there").
