Help to Fix My Computer
What "Doesn't work" about your superdrive? Is it possible to get another USB Disk Drive? 

I'm assuming that since you don't have "full" access to the other Macs that the Disk Utility app on them is inaccessible to you as well. Check on that, if you can. IF you can get into Disk Utility on one of the other Macs, you might be able to connect the two using a Firewire or Thunderbolt cable and go into Target Disk Mode to restore your Mac.

Another option would be to use the Terminal to create your own bootable USB drive. Even if its your buddy's MacBook, you should still be able to log into the App Store, download the installer for whatever version you bought, and use the built-in createinstallmedia to make a bootable drive.

If both of these options don't work, I think your next best bet is to buy an install disk off eBay or something. Hardly ideal, but then at least you'd have them if this happens again.