Some good news at last!
I went to the Leon county clerk of court website and found the document. It's in PDF format, which requires Acrobat Reader to be installed:
http://199.44.225.4/courtDockets/pdf/02-ca1970-15.pdf
Also, a summary list of all docs regarding this case can be found here:
2002 CA 1970 John C. Hill vs. Katherine Harris, et.al
(Petition to Remove Candidate Name from Ballot)
http://www.clerk.leon.fl.us/wrapper.php3?node=courts&page=/court_departments/high_profile_cases/index.html#02-1970