Further update. M-BAM downloaded and updated, thanks to what Veks sent me. It found a suspicious registry entry (Security.Disabled, or something close to that) which I had it remove. Rogue.Bat found a suspicious temp file, which it deleted just fine, after a reboot. Haven't run the ComboFix yet, but Firefox still can't access the Malwarebytes.org site.
I've been assured that the site is not, in fact, down, which would be what I would have been suspecting after all this rigmarole.