I'll try and answer the questions you had and hopefully it will help
you get it going.
WEB_ROOT should be set to the location of your sites webroot
directory, relative to your webserver's root. In your case, I think
it would be something as follows:
"/adroit/webroot/"
Basically, if you type in
http://localhost/adroit/webroot/ to navigate
to where index.php is, then that would have the above described
webroot. Most deployed environments your WEB_ROOT will just be "/",
but while developing its common to have many sites in subfolders under
your web servers web directory.
I would also ensure that your .htaccess file has RewriteBase set to
the same value as your WEB_ROOT. With those two things setup, it
should work. Also make sure that your configuration allows for
overriding the .htaccess file options if that still isn't working.