These are two different errors:
1) After changing the password, the old auto-login cookie still tries to do the login with the old password, causing repeated "login failed"-messages when trying to surf AniDB
Solution: Delete the cookie for anidb.ath.cx
2) Even though logging in on the website works at first, when then trying to view other pages (e.g. myplace), it returns a "login first".
Solution: Allow cookies from anidb.ath.cx, see
Help! Login doesn't work / kicked out when I log in.