Logo needs help - any tips for redrawing?

[hgzl]

Hi everyone!

I have this school logo (scanned in from my student id card - that's why there's a background).
I'm thinking of making some stationery or something like that with this logo.
Unfortuneately, this is the best thing i can get because the professional "redrawers" who re-drew our school logo are not allowed to give out anything. I have searched for this online...but no luck finding this logo in a better quality.

Thanks if you can give me any tips on redrawing...or something like that.(I'm a newbie)...I have Adobe Illustrator CS. (not CS2 or CS3)
Any help will be greatly appreciated!!

Thanks in advance,
HGZL