Several power supplies were swapped in and out, and since I'm doing this in a bedroom not in one of the chemistry labs at the university, I don't think there's any strange EMI. The date doesn't matter. All Macs have full support for the Y2K rollover up until the year 2019; it just sees the "7" or "07" as the year 2007. Plus, I always configure to show four-digit years, so that shouldn't be a problem. But I've sure tried it with the number of times I've reset the PRAM.

Strangely enough, when I boot into System 6.0.5, the time starts working. Then, rebooting the machine into System 7 or off of any hard drive I've tried in the machine, the time continues to work.

So I guess it's fixed? I'm not sure how or what I did. Although I'm worried it's going to stop working again after I leave it off for a while. I'm always apprehensive whenever I fix a machine without knowing what I did to fix it.