Thank You timethief for your quick response.
Before implementing any of your suggestions, now I am able to access my dashboard but gets logout automatically.
Now regarding few points you raised
1. I am logging in from the front page of wordpress.com
2. I have been using google chrome browser for the last more than one year. The version is Version 23.0.1271.95 m. It says, "Google Chrome is up to date."
3. I have deleted my cache and cookies.
4. Third party cookies enabled. I get the message, "Great, third party cookies are properly enabled in your browser"
5. HTTPS already enabled.
Currently the status is that after implementing your suggestions, I am able to access my dashboard but still gets logout automatically. I am not even able to reply to above message by timethief in my first attempt because whenever i press the "submit" button I gets logout automatically.
Thanks and Regards