Ha, I too had the pleasure of playing Metal Gear on an old CRT that had a similar bezel that covered the sides of the screen. I too had the pleasure of going crazy trying to figure out what to do. Good times.
did you continue playing after realizing this? I realized that if I punched at the edges, the sound was different if there was a door. Then it was just a matter of finding which card would open the door.
It was my cousins' game so we were playing it at his house to start with. Eventually he came over to spend the night at my house and I had a different TV that we could see the edges of the screen.