Seems so obvious in hindsight. If two machines (in this case the PAC server and the data server) were talking to each other, and you install a new program (in this case Symantec antivirus) on one of them, and now the PAC server can't talk to the data server, and the Circ app can't talk to the data server, then maybe the problem has something to do with the program you just installed, right?
I made two mistakes--well, three.
(1) I decided to update our two servers the night before our last open day before the holiday weekend. Unbeknownst to me, our vendor was closing up shop at 5 pm (MST) instead of their usual 9 pm. They still have emergency coverage of course, but I'd hate to have to drag someone away from his or her family on a holiday weekend. Next time, I'm waiting until *after* the holiday, whatever holiday it may be.
(2) I changed more than one thing at a time. On the PAC server, there were updates for Windows 2003 server and for Symantec, which has been running fine for months. In another place and time, I would have updated one at a time, rebooted, and made sure that everything was still okay before moving on to the next thing. But I was in a hurry and I had a pretty high level of confidence in both apps. So I took care of that machine and moved on to the data server, which was also ready for a Windows update.
(3) I installed a new application without confirming that everything was still working okay. Like I said, I had a pretty high level of confidence in both programs, and Symantec isn't exactly new, except to this particular machine.
Long story short, Symantec has a lot of settings. And when you install it, you get whatever the default settings are, until you go to each one and set it or leave it alone. I assumed the default settings would work just fine on my machine. (Okay, four mistakes.) The default settings caused the communication between the PAC and the data server, and between the Circ app and the data server, to slow down dramatically. After over half an hour of deliberation with the vendor, I decided to uninstall Symantec and call it a night. Except that caused the communications to cease entirely. After following a few dead ends, the vendor asked me, "what about your firewall?"
What about it? It turns out that when Symantec is uninstalled, it turns your Windows firewall on. I guess that's sort of like locking all the doors and windows before leaving on a long trip. Once the Windows firewall on the data server was disabled, everything went back to normal.
Firewall. I won't forget that word any time soon. From now on, that will be the first thing I check.
Update: Everything seemed normal when I left, but now from home, the PAC is agonizingly slow again. Working, but slow. I have no way of knowing from here whether the Circ application is still working, but I'm sure I'll find out soon.