mod_rewrite cannot make a URL "look" like anything. It cannot change the URLs in the links on your pages.
For mod_rewrite to work, the first step is to change the links on your pages to refer to the right URLs. mod_rewrite does its thing only after that link is clicked.
RewriteRule ^([a-z][a-z])/(.*)$ $2?lang=$1 [QSA,L]
Delete the first line. It's the default.
Place a slash before $2 unless you want your server hacked. Make it /$2...
The meat of the problem is this. The part that matches (.*) is passed to $2. You need to know that whatever it says, there should be a resource at the exact same path and filename inside the server in order to fulfil that request... and that's where the rule properly fails. You don't have a physical folder and file called /corporate/news inside the server.
You're trying to rewrite a URL to another URL. mod_rewrite does not do that. The right hand side of the rule should point to the actual real internal server filepath that will deliver the content. This likely includes "index.php" or some such similar filename.
Are these URL requests supposed to be handled by the core Joomla index.php file or are they handled by an extra file you've written and installed?
I'd expect to see somthing like this:
RewriteRule ^([a-z][a-z])/(.*)$ /myindex.php?path=$2&lang=$1 [QSA,L]