Hi there, Chris,
I'm sorry to hear of your problem - we have a saying in our household 'Computers are FUN, FUN, FUN!!!!!'.
A word of caution - if it is the 'C' drive, containing the operating system (i.e. Windows), you can't just transfer a loaded hard drive from one computer to another. The Windows installation process sort of tailors the operating system to that motherboard and that tailoring is further increased when the drivers are installed (i.e. chipset drivers, graphics and sound drivers, Ethernet driver etc., etc..
The following assumes that the hard drive in your poorly computer is OK.
In your situation, I'd remove the hard drive from the duff computer and either install it into an external hard drive enclosure with a USB interface or attach it to an external USB harness (they usually come with a PSU for the hard drive). Power up another computer (the 'host' computer) with lots of hard drive space available, power up the 'refugee' hard drive and then connect the USB connection. It might take a few minutes but eventually you should be able to see the 'refugee' hard drive in 'My Computer' on the host machine. (Because the host machine was booted first, it will run from its own operating system and shouldn't get confused by the second operating system on the 'refugee' hard drive.)
You should now be able to see your CNC files and stuff and copy them (NOT the operating system files!!!) over to the 'host' computer hard drive for safe keeping. You could also burn them onto a CD - this will facilitate getting them on to any new computer you get or build to replace the CNC machine.
If you now decide to build a new CNC machine, using the hard drive from the old CNC machine, the Windows installation process will include reformatting the drive. You will also need to know the identity of your new motherboard so you can get and install the appropriate drivers.
An external hard drive or two can be extremely useful in all sorts of computer manoevres, not just for back-up. So can an external harness or enclosure. We often get asked to purge the hard drives from computers that friends are scrapping - I have software that REALLY, REALLY does wipe the hard drive and I run that with the subject hard drive attached to my computer via an external harness and USB adaptor.
My lovely but shy assistant is pretty fluent with Windows and used to rescue a lot of our friends from their computer problems. She's trying to run down that activity now as we're both getting on a bit. Still, if there's anything we could do, please feel free to PM me.