You will need to log into your account on MachSupport.com and get a new license key. To do this you will need to have Mach4 installed as a demo first so you can get the new PCID for your updated computer.
MachSupport allows you to have multiple licenses and you do this process yourself without outside assistance unless something goes wrong.
This should not be an issue assuming that you remember your login information for the site.
Also you will need to save your configuration from the old installation. You can do this by copying the entire Mach4Hobby folder to the new disk drive, or you can save a "packaged profile" and restore that. The entire folder method is simpler and will insure getting other little things that may not saved in a packaged profile.
Remember that if you have not renamed your profile from the default profile name, such as Mach4Mill, it will be overwritten when you run the installer.