As Jazz has said, it's the XML (or backups) that contains all the configuration data for the machine, however what version of Windows is on the new computer?
If you open up (my) computer, right click and select "Properties", you should get a screen that shows the key properties for the computer. Is the System Type listed as 32 or 64bit?
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The reason I ask, is going by the parallel cable, I'm going to assume the parallel port is being used, which will only work on 32bit versions of Windows, and Windows 7 or earlier (the parallel port driver will not work on 64bit and/or Windows 8 onwards)
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Jazz did skip a step. When you load Mach3, do you select a profile?
If you do, is it still the exact same one as you did on the old PC?
If it is, then the XML is already in the main Mach3 folder, not the backup folder, so it's more likely to be a problem with the parallel port configuration. However, if the original machine did use plasma.xml (very bad practise!), then check the backup folder, as re-installing Mach 3 may cause the default file to of replaced the configuration file you need.
If you didn't have to select a profile on the old computer, then it means a shortcut had been created that automatically loaded the required profile (You'd need to look at the properties of the original shortcut, and the profile name will be appended to the shortcuts target).