If I submitted my site and it’s not showing up, does this mean it’s been banned?

You submitted your site [manually] [automatically] [last week] [last month] [3 days ago] and it’s not showing up in any of the search engines. Have you been penalized/banned?

If the site you submitted doesn’t have any deceptive qualities, then no, you’re not banned or penalized. However, all the submissions in the world won’t get your site listed or bring search engine traffic if there aren’t links pointing to it from other sites—and if it’s not optimized for specific keyword phrases. Submitting to search engines is not necessary nor even helpful. The search engines automatically find new pages on their own.

As with everything SEO related, the keys here are patience and time. If you don’t have both of those, you might as well get out of the SEO game right now and simply buy your way into the search engines through PPC ads.