Executive Meddling: See What Could Have Been below for most examples. Also some of the items were different including the Spinal Zap which was originally the Spinal Tap and the image in the manual was still that of an epidermic needle. With this knowledge in mind: it's easy to know why it works against the spine blocking the elevator...
What Could Have Been: LOTS. For starters: Scott Marshall (the games' creator) originally wanted to put this on Gameboy. The hero was originally going to be a black guy. The bosses were going to be smaller parts of the final boss. There were going to be useful things hidden in the lockers along with skeletons. A schoolbell would sound and flood the halls with zombie students. A different way was needed to get to the crawl space and more. This interview at bogleech.com has it all listed: 1.
To get rid of the basketballs in the gymnasium, hop up on the bleachers and destroy the scoreboard.
Once you gain access to the elevator (getting the Spinal Zap and zapping the vertebrae that guards the door), it initially doesn't provide access to anywhere you haven't been to before. To progress, hold up/left, past the fourth floor. The screen will shake for a moment, and then the elevator will open on the roof, allowing you to proceed.