In addition to
\usepackage[sectionbib]{natbib}
\usepackage{chapterbib}
You will have to put each section in a separate .tex file which you then \include. You will have to run bibtex on each .tex file separately.
N.B. Using \input rather than \include avoids unwanted page breaks, but it will not create the .aux file that BibTeX needs to do its work. I looked at the definition of \include, and I don't see how to disable the page-breaking function except by disabling \clearpage entirely. You could try
\let\originalclearpage=\clearpage
\def\clearpage{\relax}
right after your \begin{document}, but you may have to put some \originalclearpage in by hand.
