Newbie Question - Please help!

None of those sites are appear to be drupal. If you're asking if drupal can do it, yes it can. You can use the views module to create various lists of content that can then be placed anywhere, including the home page, with blocks.

_{===
"Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime." - Lao Tzu
"God helps those who help themselves." - Ben Franklin
"Search is your best friend." - Worldfallz}

It looks like the first 2 URLs are your forum and your home page, while the last one is just an example of how you want it to work. As mentioned, your main page is not Drupal, but I'm guessing you are asking because you want to convert it to Drupal.

You have a phpBB forum, which cannot directly interface with Drupal by default (it's a completely different system). What you can do though is either 1) directly query the phpBB database to get info about the posts, or 2) Install a phpBB bridge module for Drupal, which integrates your forum with Drupal. The most likely one to use is the phpBBforum Integration module.
There are a variety of other phpBB related modules you can look through here: http://drupal.org/search/node/type%3Aproject_project+phpbb

Drupal also has a forum included with it if you'd prefer to switch and have a seamless user experience on your site. You can get your forum to look and function very similar to your current one by installing the Advanced Forum module.

-- David
davidnewkerk.com | absolutecross.com
View my Drupal lessons & guides

You could create a feed of your forum using PHPBB's Smartfeed and add it to a Drupal site using the aggregator module included in Drupal core.

For recent posts and articles, you can use the Tracker module or use the views module to create a block view that you set to display on the front page only. Read up on all of these modules in the Drupal handbook or in the documentation within them to learn what they can do and how to use them.

I recommend switching over to Drupal entirely for ease of configuration and administration and more features. Your users might appreciate the Organic Groups module.

Anyway, my question is how do I get content from my forum at http://www.anxietysupportnetwork.com/index.php to display at my site's homepage...

Just to clarify some--- if the main point of your question is to integrate your forum content with the rest of the your content then you probably want to use drupal's forum (with the advanced_forum module) for ease and flexibility.

_{===
"Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime." - Lao Tzu
"God helps those who help themselves." - Ben Franklin
"Search is your best friend." - Worldfallz}