Mechanize won't cut it because it doesn't evaluate Javascript code and you really need it because the input button triggers a Javascript function. Even if you try to use Mechanize to simply submit the form, you'll get the following message:
The web site is unable to acknowledge your acceptance of the disclaimer message. This situation is typically caused when your web browser is set to prevent the use of Javascript. This site requires that Javascript be enabled in your browser. Javascript is a programming language that allows us to provide you with a richer and more enjoyable experience than would otherwise be the case. This site will not operate without Javascript.
You've got some alternatives though.