If your CNC has shielded cables then there shouldn't be any way an outside motor is going to cause problems with it running, if you are experiencing problems with the computer freezing I would look at other possible problems before investing in a different hoover
As the others have said a good earth is essential to prevent static problems, most of what I have read suggests using a star earth configuration so all earth wires run to one central point. Any cable shields should only be earthed at one end, earthing both ends will set up ground loops & cause you lots of problems.
It is worth pointing out that Mach3 doesn't play well with others so your control computer should be set up in such a way that other programs/apps don't start or carry out routine maintenance operations while you have mach3 running. Are you using mach3 with a parallel port or via USB/Ethernet ? The parallel port is probably the least stable of the 3 & most likely to be affected by other things going on.
My control computer runs mach3 & nothing else, there are no other programs installed on the machine, windows has been optimised for mach3 which basically means all the windows functions that go on automatically (in the back ground) have either been removed or disabled. The computer is never connected to the internet so there is no anti virus/malware software installed. I have been running mach3 like that for a couple of years or more using a parallel port connection & not had any problems at all, I run all sorts of other machinery at the same time as the CNC without probems. I have been meaning to upgrade to either a USB or Ethernet connection for quite a while now but only because it is generally considered to be a better set up, just never seem to have the time to get round to doing it though