Yes. those quotes are going to be a problem.
Now, I'd first loose all the <?php tags: it is going to be processed as php anyway. Just use echo for the raw html instead of switching between html and php.
Also, get into the habit of coding your queries like this
$qry1 = "SELECT TOP 3 articleID, postDate, title
FROM dbo.tblArticle
WHERE type = 'ANNOUNCEMENT' AND published = 1 AND endDate >= Getdate() ORDER BY postDate DESC";
$result = mssql_query($qry1) or die();
It makes it much easier to debug your queries by echoing the query string before you run it so you can see what you are actually passing to the db engine.
Also, you do not need to evaluate Now(): MS SQL has internal version Getdate() so you can write the query using that.
So, just write it as you would do in a normal php file without worrying about quotes and slashes etc: except without any php tags. Then use Addslashes on it.