<p>I am working on a site where users can login to get more private information.
 My client has another site else where that uses <em>nt authentication</em> for accessing it.</p>

<p>What they want to do is have a <code>button</code> on the site I am working on under the private area that will send them to the <em>nt authenticated</em> site, but not require them to log on to that site instead passing the <em>username</em> and <em>password</em> that they used to log into my site to the other site for them.</p>

<p>Is it possible to do this? and how would I accomplish it? Is there a better way to do this?</p>

How will the other site validate your username and password?
Ideally your site shouldn't even be remembering the user's password to be able to pass it to another site (you store hashes of the password, not the password itself, and only use the actually password during validation).
What if your site provided a token to the user, who presents that token to the new site, which in turn asks your site to validate the token.  Basically the second site is trusting you to tell them who the user is.
This all breaks down if the second site is actually using the Windows accounts for anything other than just retrieving a user name (for example permissions on the underlying file), since the user is not logged on as the actual Windows user account in this scenario.