The first 2 should have worked so try this, print out the hrefs to make sure it's really there:
puts page.links.map(&:href)
Remember that just because you can see it in your browser does not mean it appears in the response. It could have been sent as an ajax update. Also you can just do this which I think is cleaner:
page.link_with(:href => /menu_home/).click
However I don't think clicking that link will do what you want since it's javascript.