Yeah, I'm sorry about that! It was my typo - I was talking about configuration.php.
If there is no "live_site" variable there, you can add one, but you might not need to from what you have described in this last post.
Ok, now we are getting somewhere. Don't forget that there are two (at least!) caches involved - the cache in Joomla! and your browser's cache! This is one of the reasons I asked for the url to your site - my browser will not have any cached data for your site.
I think your problem may still be cache related from what you have described.
1) Log into the Joomla! back end, and disable the Joomla! cache and sef urls
2) log out
3) clear your browser's cache (depending upon your browser, you may even need to close it and restart it after "clearing your cash" to completely clear it).
4) Hope that your ISP, router, OS is not caching anything.
5) Restart your browser and test your site.
If this works then Joomla is essentially working correctly.
If you now want SEF urls, repeat the above process completely, except turn on SEF in step 1. and add this step between steps 4 and 5: -> 4.5) rename htaccess.txt to .htaccess
If it is not working now, and you are completely sure your caches are cleared (I always try clearing it twice and restarting the browser as I have found some browsers caches to be very "sticky"), then the problem is likely to be in your .htaccess file or that "live_site" var we talked about.
You won't need that .htaccess file unless you use SEF urls, but you will need it if you do! It might not be showing in your FTP client if you do not have it configured to show hidden files, but it should show up in ssh with ls -al. Note that for the SEF urls to work, you are looking for ".htaccess" (note the "dot").
Joomla! ships with no ".htaccess" file - the file is called htaccess.txt, and you have to rename it manually if you enable SEF urls! If you have a file named "htaccess.txt", but none named ".htaccess", then that is most certainly the cause of your trouble.
If Joomla! back end has SEF URLs set on, rename htaccess.txt ro .htaccess.
If Joomla! back end has SEF URLS set OFF, rename .htaccess.txt to something else (htaccess.txt, orig_htaccess, whatever)