Fixed it. Had nothing to do with WP.
System was reloaded and resolvers weren’t listed in /etc/resolv.conf during initial Apache startup. Resolvers were added shortly thereafter but Apache hadn’t been restarted since. PHP and/or Apache must pull resolvers once at startup; Dashboard and Akismet both working fine now after Apache restart.
I’ve experienced the same thing for the past couple days. I’m running an older version (2.0.5). Are there any connection strings that can be verified manually (i.e. via wget)?