I'm no expert, but I assume the following...
The "Key" for the OS or the game is tied to the MAC address of motherboard or eithernet card and you need an activity internet connection. When you boot your PC, Windows will connect to Microsoft's servers to validate the key and your MAC address. Once validated, you are able to go on your merry way. If Windows is not validated, then I suppose you will get a warning and Win Vista / 7 will allow you very limited usage of the PC before it automatically shuts down. Probably happens every hour or two. If I was Microsoft, I would make it every 30 minutes to annoy those people who are using pirated versions of Windows.
If your mobo dies then just call MS to release the key so that you can legitimately re-install Windows. You only do this with the OEM version of Windows. For the retail version of Windows you can re-install it as many times as you want. However, if the MS servers detects that the same key is used by more than one PC (via the MAC address) then I would assume the OS will be invalidated on both PCs and you will need to call MS to explain your mistake.
The same can be applied to games. The key you use to install the game becomes associated to your MAC address. However, publishers can even limit the number of times you install your game 'cause maybe your PC died or you uninstalled when you finished the game and then decided to play it again, whatever... I think BioShock only allowed you to install the game 5 times before you are locked out and you need to call customer support to "release" previous installs attempt so that you can install it yet again.