To the best of my knowledge, Google does not penalise individual pages. If it judges you to have broken its guidelines in some way, it will penalise the whole site - and you will be notified of the reason.
Google returns in search results those pages which it judges to most closely match the search term. If your site has many similar pages, then Google is likely to simply choose one of them to present, which is what you seem to be seeing here. If one of your pages is ranking well for the general keyword, does it really matter which one? Why do you feel it is important that it is your home page which ranks here?