Hi,
no, you don't need to buy anything new. I would however download the .062 version of Mach3 for your new PC. There is a later .066 version but it
has a few bugs, the .062 version is preferred. The only thing you really need from the old installation is the licence file named something like
Mach1Lic.dat, copy it onto a thumb drive and put it in the new Mach3 folder and you should be good to go.
Note that if you wish to use the parallel port you will have to use the 32 bit version of Win7, a parallel port will just not work with ANY 64 bit OS.
If you are thinking about using an external controller like a UC100 or Smoothstepper then use whatever OS you want, Mach3 doesn't care.
Craig