As timethief suggested above, could you please try clearing your browser cache and cookies?

http://en.support.wordpress.com/browser-issues/

Are you running any new security software that may have been updated recently to cause any changes? For example, a new pop-up blocker could be preventing the link pop-up window to work correctly.

Are you able to add an image correctly? That function also uses a pop-up box.

Instead I recommend that you ONLY log-in directly you your own blog and ONLY create posts and edit them here > Dashboard > Posts > All Posts > Add New

If you are not running one of the browsers and versions listed at http://browsehappy.com/ please try upgrading or switching first.

Note: If you are using an IE9 browser in compatibility mode that makes it render as IE7 and IE7 is not supported. To disable see > http://www.sevenforums.com/tutorials/1196-internet-explorer-compatibility-view-turn-off.html

If you are, please do these four things:

1. Try clearing your browser’s cache http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=32050

2. Make sure that you have third-party cookies enabled http://en.support.wordpress.com/third-party-cookies/

3. Try with all browser extensions or add-ons temporarily disabled.

4. Try enabling HTTPS: http://en.support.wordpress.com/https/

If you are not successful let us know which browser (and version of it) you’re using and post any error reports you get.

I tried different browsers, other sites I have and the same things happens everywhere.

It worked yesterday. Anything you can offer is appreciated.

Enter the anchor text you want to link to first.
Then use your mouse to highlight that anchor text.
Next click the chain icon in the editor and proceed to create the link.