I searched around, scrolled through the generated CSS coming out of Moodle, and found that there was no closing brace before the SyntaxHighlighter CSS was inserted! I then looked at settings.css in the theme's style folder, and sure enough, there was no closing brace. I put the closing brace in, and SyntaxHighlighter worked like a charm!
I know there's also probably a better way to implement Syntax Highlighter, but I just thought I'd share this.
You can get SyntaxHighlighter here: http://alexgorbatchev.com/SyntaxHighlighter/