I want to use Press Releases as the basis for articles on my web site.

Are Press Releases in the Public Domain? If so, can I use some of the
web based "newswire" organizations to find content related to my web
site?

The short answer is no, press releases are not in the public domain. 
The copyright to the press releases is likely owned by the company
that issued the press release, and you should obtain permission from
the owner of the copyright before reproducing the article elsewhere. 
There are exceptions, like the fair use doctrine, that may permit you
to use the press release without permission and avoid liability for
copyright infringement.  See http://www.copyright.gov/fls/fl102.pdf. 
This is why news reporting organizations can reproduce and publicly
display press releases.  But rather than rely on a perhaps erroneous
assessment that yours is a fair use, you should seek permission.