...ahah. So I'm not the only one dealing with this.
I HAD been using a quickfix of starting the launcher while disconnected from the internet; when the normal error box of "cannot reach the server" popped up, I'd tell it to start the EVE client directly (without going through the launcher, where the issue appears to be). With a new patch coming tomorrow, however, I suspect I'm going to have to just re-download the EVE client.
In my case, at least, the issue appears to have been triggered by dealing with a network which, while publicly accessible, redirects all traffic to a browser-based logon page. One day I accidentally started the launcher before authenticating myself in a browser. It appears that CCP coded the launcher for two situations - it cannot connect to a network at all, or it can successfully reach the server. That it could connect to a network but be redirected instead of reaching the server was not coded for, thus causing this error. Annoyingly, the client then became stuck attempting to contact the authentication server, even while my PC was literally plugged into the wall instead of connected wirelessly.