Main Problem
This is for a domain "collierhills.net".  I tried to set a general redirect from "www.collierhills.net" to "collierhills.net".  Here is the code I put into the root .htaccess file:This redirects to "collierhills.net/public_html/" and throws a 404 error.  I've tried several things without success.

Herlp!

Smaller Problem
I tried putting the code above (or some variation) in both the root .htaccess and the /public_html/.htaccess files.  Both gave me the problem above.  Now, however, when I take out the Rewrite code, I get the same problem!  It still redirects, only to the /public_html/ file.  In other words, I can't just change it back -- "www.collierhills.net" doesn't work at all.

I very much appreciate your trying to help, but most of the answers to your questions are in my post.  This is a primary domain "collierhills.net".  And I agree, it ought to work. 

The "root .htaccess" is simplay an .htaccess file in the root directory.  I tried putting the redirect in the .htaccess file for both the root directory and the public_html subdirectory.  The idea is that it will redirect the browser to the url "collierhills.net" which will automatically load the following url: "collierhils/index.php"; that is, to the url determined by the server path "root/public_html/index.php".  Instead, it redirects to the actual url "collierhills/public_html/..." 

I hope that's clear.
User types "collierhills.net" -- user gets the url "collierhills.net/index.php", which is determined by the server path "/root/public_html/index.php".  Right?
But when the user types "www.collierhills.net -- user gets the url "collierhills.net/public_html/..." which is nonexistent.
I don't know what else to say.  I type "www.collierhills.net" in my browser and I get a 404 error saying "collierhills.net/public_html" is not available.  For some reason it is reading the public_html directory as the url instead of the source.

This may be an Apache configuration bug -- I'm going to send a ticket.

Level I - Root Directory (collierhills.net)
   .cpanel      755
   .cpanel-datastore      700
   .fantasticodata      755
   .gnupg      700
   .htpasswds      755
   .trash      700
   access-logs      750
   etc      755
   mail      770
   public_ftp      750
   public_html      750
   tmp      755
   www      750
   .bash_logout   0 k   0644
   .bash_profile   0 k   0644
   .bashrc   0 k   0644
   .contactemail   0 k   0600
   .ftpquota   0 k   0600
   .lastlogin   0 k   0600
   mysql_articles_edit.php   0 k   0644
   mysql_articles_login.php   0 k   0644
   mysql_articles_user.php   0 k   0644
   mysql_roster.php

/root/public_html/:
   cgi-bin      755
   chforum      755
   greystone      755
   guestbook      755
   images      755
   includes      755
   mixble      755
   px800      755
   snippetmaster      755
   test      755
   ---
   .htaccess   0 k   0644
   Thumbs.db   86 k   0644
   about.php   4 k   0644
   crumbs.inc.php   0 k   0644
   error_log   2 k   0644
   gallery.php   3 k   0644
   index.php   5 k   0644
   newsletter.php   7 k   0644
   path.php   9 k   0644
   php.ini   0 k   0644
   simple_template.php   0 k   0644
   style.css   5 k   0644
   template.html   1 k   0644
   template2.html

I haven't done anything fancy. There is no subdomain, parked domain, or add-on domain in the account.  I have removed .htaccess from the root directory and placed it in the public_html subdirectory.