Pings at last!
Thank God Almighty, pings at last! Since this blog's inception, I haven't been able to automatically ping blo.gs and weblogs.com. MT would say it pinged, but I wouldn't show up on either site. I noticed that I was able to ping from another MT installation on the same server, and realized that I downloaded the whole package with libraries for that install. A quick copy of the full extlib folder fixed my problem right up. So, in the end, my pinging problem was an incompatible version of one of the libraries.
Hopefully this will help anybody else whose pings aren't working. I looked all over the web and never found a good answer for my problem.