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Certainly there were manual milling machines and turret lathes before there were computer controlled versions (and there still are of course) . There were also automatic turning machines (screw machines) that used cams and hydraulics, before there were electronic NC (Numerical Controll) which in turn predated CNC (Computerized Numerical Control)
But as far as running a modern turning center with the computer disconnected or otherwise inoperable, I don't think so, I doubt any have a mechanical manual mode, any manual, jog or teach mode probably does rely on the computer. For a milling center, some of the smaller ones (job shop type) may have the possibility for direct manual control, but for big production machines, I'd think it is unlikely, but this would depend on where one makes the distinction between "machining center" and "CNC mill" (the mill may well have manual handwheels)