Yeah, I know the frame is trashed. What I meant by welding on a cog, is to weld it to an old 27" wheel. If I did that, the money I'd have into the bike would be the cost of the cog, which isn't too bad.
As far as my school. It's not really the school, but the neighborhood it's in. I'm not so much worried about outright theft, but the 'locals' aren't very respectful of students and it's not uncommon for all of the bikes on a give rack to be kicked over or whatever. It wouldn't bother me on an $8 bike.
Thanks for the advice. I'll check to see if any of the 27" wheels I have sitting around is even close to true, then weld a cog on. Then I suppose I'll be set.
Thanks for putting up with my questions, hahaha.