Keychain First Aid won't repair and will ask me for keychain agent password

Question

Hi everyone:
Background: I changed my Apple Id password after updating to OS X Mavericks. Soon after that, OS X sometimes asks me for keychain password (not always), sometimes at the beginning and when I use Safari, or try to access to Icloud (which I can only access online on safari) through system preferences.
Problem #1:
-  When I use First Aid Keychain and enter my User name and password, two options appear: Verify and Repair.
- If I hit verify, some things appear in black, some other in red and some in blue, the following things appear:
    In red:
         ~/Library/Keychains/login.keychain (is not a valid keychain file).
   In Blue:
        Keychain password of  ~/Library/Keychains/login.keychain (100022) not verified
       Adjustments of  ~/Library/Keychains/login.keychain (100022) were not read (couldn´t been read)
  In Red
        ~/Library/Keychains/login.keychain (-25295) was not opened (couldn´t been opened)
  Problems have been found. Select repair.
  Verification error.
- Then, if i hit repair It will ask me "for keychain agent password".
And honestly I never (that I remember) created a keychain agent password. Where can i find that?, what kind of password is that? What I know is that it is not my Apple Id password or anything close to it.
Problem #2
- If try try to restore my default keychain by selecting Preferences - General, it will tell me that the "keychain has not been found". And wont restore anything.
I must say that I have read many of the discussions available and many of Apple suggested solutions, and nothing seems to help.
Any help would be deeply apreciated.
Best regards. (Sorry for my english, not a native speaker, my computer is in spanish and did my best to translate what I have seen)
Macbook Air, OS X 10.9, 2 GHz Intel Core i7, 8GB 1600 Mhz DDR3

Answer 1

Hi John (it´s me again sorry!)
I did what you suggested using Safe Mode (I actually did it following http://support.apple.com/kb/PH14204 for oS X Mavericks).
I followed the same steps that I have done before;
- Before deleting I used First aid Keychain and what I got was the following:
- Then I hit repair and I got the following:
- After that I decided to delete Login Keychain (the empty square), it was gone. I restarted my computer in normal mode. Once I did that what I see now is the following:
- Maybe I missed something, and I still cant see the padlock in login, and no way no decipher whats going on.
PERHAPS THE FOLLOWING IS RELATED:
- If try log into ICloud through System Preferences the following pops up after entering my Apple ID and Password: 
- If I select Reset to Defaults I get the following (even if I select cancel):
- And after that I get the following:
Could that be related? Thank you very much again and sorry for too many images.
All the best!