And there is your problem. .html are static HTML files. You have to have them named .php for them to be parsed by the PHP parser.
It can be done, but I wouldn't advise that. It adds unnessary load on the server when all you want is a static HTML file.
To accomplish what you want, add this to the .htaccess file. However, like I said, you do NOT want to do this as it will cause an increased load on the server (increased load == SLOW website):
Action php5 /cgi-system/php5.cgi
AddHandler php5 .html
Like I said before, and I stress this again, HTML files are for static files. They are your quick load files that do NOT get parsed by anything (although some people will parse them through SSIs). They are NOT meant to be used for PHP parsing. That's what PHP files are for (.php).
yerba# rm -rf /etc