I have similar setup with Hypertherm 45 and candcnc DTHC (MP-3000). It took me few days to set-up everything right.
The point you may check is if your serial comm is running --> on MACH3 main screen the DTHC up should lite green all the time. If not, check your settings in win/control panel. Maybe IRQ conflict as it was my case.
Reply if you have found a solution.