The repair mostly will take good schematic diagrams and good troubleshooting information in the manuals, and good test equipment (logic probes, oscilloscopes, and other such things.)
As for fitting a newer control -- look into the EMC package running on a modified linux kernel with a real-time sub-kernel which runs the normal kernel as one task. The software is free. It runs on boxen which used to be Windows boxen. If the mill in question has servo motors instead of stepper motors, you will probably need something like the Servo-2-Go board (which can handle eight axes at need. Three for X, Y, and Z, another for spindle speed, and two more for something like a two rotary tables at right angles to each other. :-)
Well ... my Bridgeport Series I (BOSS-3) CNC mill has the X-axis leadscrew (ball screw) locked stationary, and the nut is rotated around it in the saddle. This suggests that there is no practical way to fit handwheels to the existing leadscrews. The Y-axis one does rotate, but there is no exposed way to rotate it unless you take the cover off the belt guard and fit a handwheel.
I don't know the Series II -- other than that it is larger. And the Heidenhein controller is newer than what my Series-I came with, which was a Bridgeport home brewed one built around a LSI-11 CPU and some custom wire wrap boards (which were later replaced with printed circuit boards).
The price sounds good, if you can move it and have room for it, and with your familiarity with linux, the EMC package is probably the way to go.
Good Luck, DoN.