Vorzeigen, it sounds like you might have a had a slight crash??? I have had this happen a couple of times on our 1990 Conquest machine as well after a light crash (usually after a broken parting tool and the next tool crashing into the un-cut part still left on the bar.) I only know how this is done on our machine - a 1990 Conquest SP. I have heard that the later ones can actually be done without any mechanical work, just a series of button pushes and a turn or two of the MPG wheel, but I really don't know for sure.
Our machine has a torque limiting coupler between the axis motors and the ball screws to limit the damage. Fortunately it's pretty easy to re-couple the ball screw and motor if you have the Hardinge tools; I was lucky in that these came with my lathe when I got it a number of years ago. Basically you remove the large sheetmetal cover on the left side of the machine that covers the spindle/collet actuator. This gives you access to where this stuff is located, which is between the Z axis motor and the head wall sheetmetal (separating the mechanicals and the cutting area.) There is a small fan (~100mm) mounted on a plate, remove the screws from the top and there are two screws that come in from the cutting zone - I think they might hold the Z axix cover on also, can't recall without looking though; set this aside. There is a small cover with a proximity switch mounted on it - this switch is what signaled the alarm when the coupler became de-coupled. Here is where it gets a little tricky, there is supposed to be alignment marks on the end of the motor shaft and the end of the ball screw shaft, but I can only find white paint makes that appear to be sloppily applied, which I did not believe to be from Hardinge, but from the previous owner. Anyway, you can reach in and turn the motor shaft and the ball screw easily to align, all with the use of an inspection mirror of course as the hole faces skyward. Once aligned, then the Hardinge tools come into play, a "base" piece mounts to where the inspection cover came off, and then a "fork-like" tool pivots off this base to spring the coupler back together. Even with the tools, it's tough as access is really limited. I believe that after it's back together, you will have to turn off the control and re-home the machine, that's about all there is to it.
Unfortunately, if you don't have the tools, it's going to be a tough road, so I would suggest finding an old Hardinge service engineer that has the tools, and pay him for the few hours or so the whole job should take. I think I can do in it less than an hour from bump to cutting parts, so a real tech should be faster than me....
Sorry for the long winded response.