The FIX:

Here's what I've found - Windows 2003 does some WIERD stuff with the file permissions during the installation process.  First, I was having a different issue with the whole "Running Database Scripts" hanging up at that "4.4.0" update or whatever like many other people when trying to install 4.5.5.   I noticed that it completed all the steps one time through, but when clicking Next, it apparently forgot that it had just run all the scripts and when it tried it again, it hung up.

So I scrapped the whole 4.5.5 and downloaded 4.8.  This time, I got past that with no problems, but now I was having the EXACT same problem installing modules that you mention here.  Through my other battles, I noticed that every time I went to the directory security for the web site's folder, the "Read Only" box would always be checked.  I would have to uncheck it and click OK.  Otherwise, despite the correct NETWORK SERVICES permissions, the whole folder would be Read Only. This actually caused an issue at the beginning of the installation where I would get an error message about "cannot write to web.config".  Apparently, the installation process modifies the folder permissions, and when it does this, Windows 2003 (at least my installation) keeps reverting back certain file permissions.

SO.... with that in mind, my installation was stuck at the selecting modules screen with the errors.  Clicking Next just returns the same errors.  I went back over to the web server and opened up Properties on that folder.  I deselected the "Read Only" checkbox, then went over to the Security tab and double checked all permissions there - everything was good.  Next, I went into the Advanced screen (click the "Advanced" button on the Security tab).  I checked the "Replace permission entries on all child objects..." check box and clicked OK to FORCE these settings all the way down the ranks.

After forcing the permissions down, I went back to the setup screen that had the module errors, clicked Next, and POOF!  It worked.

Wierd permission things going on with Windows 2003 as near as I can tell...  The trick is to FORCE the permissions to propegate back down to all files and subfolders.