Can't run games from disc. HELP!

The question remains: why can I no longer play games from a physical disc? When I attempt an installation and try to launch it, the system claims it isn't compatible. Yet, I was able to play them perfectly fine before. Where does the fault lie?

Wait, weren't you running Windows XP before? Maybe you switched over to Windows 7?

I had Windows 7 on my previous machine, just like I do now. Even after a fresh installation onto the C drive, the same issue persists.

The answer is actually pretty straightforward: some of these newer titles specifically require a 64-bit version of macOS, and since you're running a 32-bit setup, they just won't launch. If you were playing these exact same games without any issues before, I'm almost certain you had the 64-bit version installed back then, and somehow—maybe during an update or a fresh install—the 32-bit version ended up on your machine instead. You'll likely need to wipe things and perform a clean install of the 64-bit OS to get everything running smoothly again.
P.S. Just a heads-up, besides the OS requirement, a lot of modern games also demand a graphics card that supports DirectX11, otherwise, you'll hit a wall there too.