System Requirements: The system requirements for the game are extremely modest: it will run just fine on a 266mhz Pentium II with 128 MB of RAM. Since it just shows pre-rendered images, you don't have to have a graphical accelerator card or anything like that.
To put this very simply, if you can run Windows, you can run The Key. I have tested The Key on Windows 95, 98, ME, 2000, NT, and XP and it runs just fine on all of them. It won't run on Linux or on a Macintosh, though, so if that is your system you are just out of luck.
Since The Key uses sound effects, it does require a sound card. It might run without one, but you'll get strange errors and see other odd things happen. If you don't have a version of DirectX installed, you'll need to install it to get Part III to work: Part III uses some .mp3 files as sound effects, and DirectX is required to play them.