Thanks for the reply Braulio. I conatcted the administrator and was
given the mail server name. I was told I do not require user id and
password. So, in my web.config I added:
   <system.net>
     <mailSettings>
       <smtp>
         <network host="mailrelay.agencyname.gov" />
       </smtp>
     </mailSettings>
   </system.net>

and in the aspx file:

   protected void Button1_Click(object sender, EventArgs e)
   {
       string strFrom = "me@here.com";
       string strTo = "you@here.com";
       MailMessage mm = new MailMessage(strFrom, strTo);
       mm.Subject = "Test Email from ASP.NET";
       mm.Body = "This is a test email sent from within an ASP
application.";
       mm.IsBodyHtml = false;
       mm.Priority = MailPriority.Normal;
       SmtpClint sc = new SmtpClient();
//        SmtpClient sc = new SmtpClient("mailrelay.agencyname.gov");
//        sc.Credentials = new NetworkCredential();
       sc.Send(mm);
   }

I get an error from Symantec Email Proxy:

Your email message to you@here.com
with mail subject of
Test Email from ASP.NET
was unable to be sent because the connection to your mail server was
interrupted.
Please open your email client and re-send the message from the Send
Message folder.

I tried changing the web.config to read:
<network host="mailrelay.agencyname.gov" userName="" password=""  />
but got the same error.

Thanks.