That is not good news, the com port is a serial port. Mach3 is designed to control the parallel port.
I have converted a couple of other machines that were formerly com port driven. One was a D&M cnc lathe, all it required was a little rewiring and some filter caps on the driver boards to get rid of noise, and a lot of research, the driver boards were an obsolete ic that had no data sheets to be found on the web, it was all ttl logic though. The other was a cnc router, forgot the mfg, it required a couple of Gecko servo drives for the x & y, a stepper drive for the new stepper on the z, and interface boards. The old controls were a ISA control board in an old AT machine that was long lost, and a DOS based programming software.
First glance yours could be converted, you are probably talking around $500 or less in parts, for driver boards and interface.
If you machine has a mfg web site post a link here and your full model number and I will take a look for you.
Arnie