Thank you to everyone who took the time to read and provide some advice- it is much appreciated

After much head-scratching, crying and pleading we finally got to the bottom of things. The parallel port on the new PC was just not outputting any signals. Whether that was due to the port being busted or Mach3 just not getting along with it I'm not sure. I used this video to get started https://www.youtube.com/watch?v=uglCm_qsojk

After some suspect prodding about with a paperclip and a multimeter, I coaxed my friend over with the promise of food and coffee and he brought his oscilloscope to confirm that mach3 and the parallel port were not cooperating. I bought a UC100 motion controller to bypass the whole thing- I really do recommend one of these, well worth the money.