I knew there was a reason that I took "Auto Electrical" this semester... If the black wire came from the positive side, I don't know.... but as mentioned, if it came from the negative (which it should if it's black) then find a place on the frame.
If the wire was on the positive side and ran to ground, it might have been draining the battery constantly... but that wouldn't explain it only draining while "on".
You can run to ground on any ground, whether it be the frame or another cable running to ground (probably a better idea to go to the frame though). Don't run the positive straight to ground.... not a good idea. I don't know why the battery would go to a fuse... if so, it'd probably be in the fusebox, but honestly I wouldn't be surprised if they put an inline-fuse in there. Anyhoo, I'd just check and make sure the battery is good, hook it up (making sure to get the positive and negative connected right) and check fuses.
I'm thinking it's a fuse or loose connection, especially if it wouldn't roll start... hopefully it's nothing worse. Good luck with it