This turned out to be a hardware problem. There's a sound board in my laptop, which was defective from the start. I was able to order a replacement part and swap it out. I wasn't able to diagnose the actual cause of the defect. I suspect either the board had some defect in it causing a line to short, a component (maybe a transistor or voltage regulator) was defective, or a chip wasn't soldered in properly. Electronics nowadays are so fine and small, it's almost impossible to repair yourself.
Normally, I would have returned it for a replacement, but I moved to Germany, and this laptop had no support in Germany. So I had to replace the part at my cost, even though the laptop was defective from the beginning. Just something people should be aware of if they're buying laptops and taking it somewhere else in the world. I believe this isn't a problem with Apple products.