well thats a nice lot of knitting you have there just my cup of tea but I have been a long time sorting bigger piles of knitting  

but thats me
you have a lot of custom boards in there , I will bet they will not give you any info as to the specs
what you need to do is get a large note pad pencil or biro if you are confident
get the spec of all the axis motors ( I use that because they could be servos or steppers  they may even be 3 phase servos ) 
set the HP voltage of the spindle and check if the control has a VFD , but that may be a servo as well
IMHO you would need to junk 90%  its going to get spendy quick with no guarantee of success 
have you approached the manufacturer to see if they do a control upgrade 
I would estimate that that machine will be out of service for 3 to 6 months if you try to do the swap out 
just my 2 cents but I wish you well in your endeavours 
to your last question there is no such thing as a mach3 or mach4 mother board. m3 and m4 run on a standard windows pc nothing special at all Mach3 or Mach4 is just a program that runs on the PC