Here is more information after more testing:
First, I confirmed that in IE7 (which is what I have on my laptop), my server is automatically detected as a "Local intranet" site. I can tell becuase at the bottom of the IE window it shows the zone in which this site is operating. I also confirmed that the security settings for the Intranet zone are set to "Automatically login only in the Intranet zone". I believe if this were not the case, even navigating to the http://myserver/admin/security/WindowsSignIn.aspx URL would not work.
With that confirmed, I tried to make headway on automatic login by visiting the URL http://myserver (rather than having to add the specific path to the Windows login page).
NOTE: After each of the changes below, I restarted the IIS Admin Service just to be sure there were no residual effects of the previous configuration.
First, I tried changing <authenticaltion mode="Forms"> to <authentication mode="Windows">. Specifically, I commented out the existing section in web.config and uncommented the section after:
<!--
<authentication mode="Forms">
<forms name=".DOTNETNUKE" protection="All" timeout="60" cookieless="UseCookies" />
</authentication>
-->
<identity impersonate="true"/>
<authentication mode="Windows">
</authentication>
This had an adverse effect. All I get now when loading http://myserver is the following error:
DotNetNuke Upgrade Error
The Assembly Version ( [ASSEMBLYVERSION] ) does not match the Database Version ( [DATABASEVERSION] )
ERROR: Could not connect to database.
A connection was successfully established with the server, but then an error occurred during the login process. (provider: Shared Memory Provider, error: 0 - No process is on the other end of the pipe.)
I undid my changes, and it reverted to the previous behavior. So that part, at least, is reproducible.
Next, thinking that the problem may be due to the <identity impersonate="true"/> tag, I left it commented out. In this case, I reached the Home page, but I was not logged in. Additionally, entering the URL http://myserver/admin/security/WindowsSignIn.aspx also did not log me in.
So, in conclusion, I have not been able to confirm any configuration that allows automatic login without visiting the URL http://myserver/admin/security/WindowsSignIn.aspx. I am happy to try any ideas other may have.