@Beltboy
Good news!
I managed to get to my desktop without it shutting down. I had my PC running for 5-10 minutes just to make sure that it wasn't going to shut down unexpectedly.
The bad news is that at first it beeped for 2-3 seconds then stopped, then again, and then again. Then a 10 second pause and then it kept beeping until I shut down my PC. It did not shutdown by itself, but it kept beeping.
So, now I think that the problem is more like software-based. I can confirm that everything worked and functioned as expected. The problem might be that the system is reading/missing something wrong and thus making the beeping sound in order to warn me.
I plan on running the PC for a straight 2-3 hours doing medium-light workloads. If the system does not shut down on itself but still keeps beeping, I plan to remove the built-in speaker.
I know that this is not a good idea, but it's the only option I have.