Today was that day.
It was a combined effort, including learning how to get molly bolts to work.
The instructions that came with the cabinet (or at least the English version of them) called for me to drill through the top beam of the cabinet to fasten it to the wall. After careful probing, I was able to determine there were no studs where I could use them. The one stud in the middle of the cabinet was directly under the hinge between two of the three doors, thereby forcing me to use molly bolts, or screws with sockets you sink into the wall.
I drilled the pilot holes as Warren held the cabinet in place. I then changed bits and drilled the holes for the sockets while he went into the den and sat, riding out one of his seizures. I had to abandon one of the bolts because I drilled too close to the stud and the whole thing shoved to the left and wouldn't come out of the wall. I opted to counter-sink it so it wouldn't interfere with the cabinet, which officially only "needed" two screws anyway.
Figuring it'd be a while before Warren was able to help again, I tried screwing in the bolts. Problem: The screws weren't staying in the bolts. It turned out the screws needed to be about half an inch longer to secure into the sockets.
Warren then appeared. He saw what was wrong, and luckily, he knew where I had more molly bolts of the same screw width but with longer screws. We used them, they worked, and now I have a medicine cabinet. Yaay!!!