You could do something like this with CSS Form Builder or the Validation Toolkit. Using client side validations you can have have areas on the form hide or show based on the validation of a form element.
For example, if you applied a client side required validation on the checkbox, you would then apply a show/hide validation response that will make another part of the form visible.
I'm including a sample page of what this type of setup looks like as an example. Please post back with any questions that you have about any part of this.