what I\'m trying to do is converting a TextArea content into a valid html code. Suppose you type inside the TextArea and then you press a button that shows the typed text inside
Consider looking into a markdown editor. Stack overflow uses a modified version of this one: http://wmd-editor.com/
Well, it's not very difficult:
$('#element').html($('textarea').html().replace(/\n/g, "<br />"));
With the appropriate styling on the element, you shouldn't need to convert anything. Using the CSS white-space property with a value set to pre, any white-space in the element should appear exactly as it does in the textarea:
#myElement { white-space: pre; }
Example: http://jsfiddle.net/TkpSu/