New data:
The access log does insert a line if I use the IP address instead of the domain name. It reads:
12.7.243.234 - - [26/Jul/2000:14:06:28 -0400] "GET /test.html HTTP/1.1" 302 243 "" "Mozilla/4.0 (compatible; MSIE 5.0; Windows NT; DigExt)"
However, the server.log doesn't log any activity at all.
I think this tells me that the DNS isn't quite right.
Like I said earlier, I've checked into it. However, I want to double check--each hop doesn't need to know the domain name, right? I mean, the client needs to have access to a DNS entry that says what the IP address is, but the 17 other hops (in my case) don't really care about that, right?