Your example has no chcekbox. It's just a parameter passed back to CGI. The submit button has no associated form. How do you propose to do anything with CGI here? I suggest you read and understand the documentation for the tools you've chosen to use, and make more effort when asking for help.

If this is a real example of something you're trying to do then Perl can't help you here. Everything is client side. Use JavaScript.

Update: Strike out, substantial edit.