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http://tweetdeck.uservoice.com/pages/1192-general/suggestions/101269-unable-to-login-with-twitter-username-and-password-
I had the same problem - I couldn't get tweetdeck to authenticate with Twitter after I'd changed my Twitter password. Very frstrating, but I fixed it by;
1. shut down tweetdeck
2. follow tweetdeck on twitter by clicking on "Follow us on Twitter" link at http://tweetdeck.com
3. then followed these instructions as provided by Richard Barley;
1. Log out of TweetDeck using the triangle "Log out" button in the top-right
2. Restart TweetDeck
3. Click the link "Click here if this is the first time you have used TweetDeck on this computer"
4. Enter your TWITTER userid and password and click Add Account
5. On the "Register for a TweetDeck Account" screen, click "I already have a TweetDeck Account"
6. Enter your TWEETDECK userid and password and click "Verify Account"
7. Import any columns if it prompts you, otherwise just click Finish.
Now working as it should. HTH. Good luck.