I have got a WordPress site installed here: http://www.r-bloggers.com

And If only to set up another WordPress site underneath the /lang directory:

http://www.r-bloggers.com/lang/

I produced the subfolder and submitted the files, however when I visit the folder, the website keeps saying it is a 404 page from the root directory website.

I picture this has something related to the mod-rewrite rules within the .htaccess. Following a directions here I attempted and adding these line:

RewriteCond /lang/
RewriteRule . /lang/index.php [L]

However it did not help...

This is actually the exact re-write rules within the .htaccess file:

# BEGIN W3TC Browser Cache
<IfModule mod_deflate.c>
    <IfModule mod_setenvif.c>
        BrowserMatch ^Mozilla/4 gzip-only-text/html
        BrowserMatch ^Mozilla/4\.0[678] no-gzip
        BrowserMatch \bMSIE !no-gzip !gzip-only-text/html
        BrowserMatch \bMSI[E] !no-gzip !gzip-only-text/html
    </IfModule>
    <IfModule mod_headers.c>
        Header append Vary User-Agent env=!dont-vary
    </IfModule>
    AddOutputFilterByType DEFLATE text/css application/x-javascript text/html text/richtext image/svg+xml text/plain text/xsd text/xsl text/xml image/x-icon
</IfModule>
<FilesMatch "\.(css|js)$">
    FileETag None
    <IfModule mod_headers.c>
         Header set X-Powered-By "W3 Total Cache/0.9.1.3"
    </IfModule>
</FilesMatch>
<FilesMatch "\.(html|htm|rtf|rtx|svg|svgz|txt|xsd|xsl|xml)$">
    FileETag None
    <IfModule mod_headers.c>
         Header set X-Powered-By "W3 Total Cache/0.9.1.3"
    </IfModule>
</FilesMatch>
<FilesMatch "\.(asf|asx|wax|wmv|wmx|avi|bmp|class|divx|doc|docx|exe|gif|gz|gzip|ico|jpg|jpeg|jpe|mdb|mid|midi|mov|qt|mp3|m4a|mp4|m4v|mpeg|mpg|mpe|mpp|odb|odc|odf|odg|odp|ods|odt|ogg|pdf|png|pot|pps|ppt|pptx|ra|ram|swf|tar|tif|tiff|wav|wma|wri|xla|xls|xlsx|xlt|xlw|zip)$">
    FileETag None
    <IfModule mod_headers.c>
         Header set X-Powered-By "W3 Total Cache/0.9.1.3"
    </IfModule>
</FilesMatch>
# END W3TC Browser Cache

# BEGIN W3TC Page Cache
<IfModule mod_rewrite.c>
    RewriteEngine On
    RewriteBase /
    RewriteCond %{HTTP_USER_AGENT} (2\.0\ mmp|240x320|alcatel|amoi|asus|au\-mic|audiovox|avantgo|benq|bird|blackberry|blazer|cdm|cellphone|danger|ddipocket|docomo|dopod|elaine/3\.0|ericsson|eudoraweb|fly|haier|hiptop|hp\.ipaq|htc|huawei|i\-mobile|iemobile|j\-phone|kddi|konka|kwc|kyocera/wx310k|lenovo|lg|lg/u990|lge\ vx|midp|midp\-2\.0|mmef20|mmp|mobilephone|mot\-v|motorola|netfront|newgen|newt|nintendo\ ds|nintendo\ wii|nitro|nokia|novarra|o2|openweb|opera\ mobi|opera\.mobi|palm|panasonic|pantech|pdxgw|pg|philips|phone|playstation\ portable|portalmmm|ppc|proxinet|psp|pt|qtek|sagem|samsung|sanyo|sch|sec|sendo|sgh|sharp|sharp\-tq\-gx10|small|smartphone|softbank|sonyericsson|sph|symbian|symbian\ os|symbianos|toshiba|treo|ts21i\-10|up\.browser|up\.link|uts|vertu|vodafone|wap|willcome|windows\ ce|windows\.ce|winwap|xda|zte) [NC]
    RewriteRule .* - [E=W3TC_UA:_low]
    RewriteCond %{HTTP_USER_AGENT} (acer\ s100|android|archos5|blackberry9500|blackberry9530|blackberry9550|cupcake|docomo\ ht\-03a|dream|htc\ hero|htc\ magic|htc_dream|htc_magic|incognito|ipad|iphone|ipod|lg\-gw620|liquid\ build|maemo|mot\-mb200|mot\-mb300|nexus\ one|opera\ mini|samsung\-s8000|series60.*webkit|series60/5\.0|sonyericssone10|sonyericssonu20|sonyericssonx10|t\-mobile\ mytouch\ 3g|t\-mobile\ opal|tattoo|webmate|webos) [NC]
    RewriteRule .* - [E=W3TC_UA:_high]
    RewriteCond %{HTTPS} =on
    RewriteRule .* - [E=W3TC_SSL:_ssl]
    RewriteCond %{SERVER_PORT} =443
    RewriteRule .* - [E=W3TC_SSL:_ssl]
    RewriteCond %{HTTP:Accept-Encoding} gzip
    RewriteRule .* - [E=W3TC_ENC:.gzip]
    RewriteCond %{REQUEST_METHOD} !=POST
    RewriteCond %{QUERY_STRING} =""
    RewriteCond %{REQUEST_URI} \/$
    RewriteCond %{REQUEST_URI} !(\/wp-admin\/|\/xmlrpc.php|\/wp-(app|cron|login|register|mail)\.php|wp-.*\.php|index\.php) [NC,OR]
    RewriteCond %{REQUEST_URI} (wp-comments-popup\.php|wp-links-opml\.php|wp-locations\.php) [NC]
    RewriteCond %{HTTP_COOKIE} !(comment_author|wp-postpass|wordpress_\[a-f0-9\]\+|wordpress_logged_in) [NC]
    RewriteCond "/home/rblogger/public_html/wp-content/w3tc/pgcache/$1/_index%{ENV:W3TC_UA}%{ENV:W3TC_SSL}.html%{ENV:W3TC_ENC}" -f
    RewriteRule (.*) "/wp-content/w3tc/pgcache/$1/_index%{ENV:W3TC_UA}%{ENV:W3TC_SSL}.html%{ENV:W3TC_ENC}" [L]
</IfModule>
# END W3TC Page Cache

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteCond /lang/
RewriteRule . /lang/index.php [L]
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>

# END WordPress