I don't think it's possible to "rebuild" the power supply. I think you could replace the power supply with a PC power supply and an additional 24V supply.
Find the color code of the wiring in the Hurco. I don't know if this changed from the old BMC's and KMB's that I know. The color codes for the older machines are Here.
Hook up the PC power supply to +12, +5, -12. You'll need to trick the PC power supply to turn on. There should be notes on the web to do this. The notes should also cover the color codes of ATX power supplies.
Get a 24V supply. Hook it up to +24 on the Hurco. Make sure it can handle the load. I'd get as big a 24V supply as I could find, at least 5 Amps, 10 is better.
Connect the 0V/DC return of the power supplies together, and to the Hurco's 0V.
Bear in mind that a PC power supply won't run with no load.