When you log into your Windows 7 computer you cannot log in and you receive the message - 'The trust relationship between this workstation and primary domain failed'.  This will happen when connected to the LAN, however when not connected to the LAN you can login fine.
Not sure exactly what causes it yet but I have used the following workaround by combining a few articles I have come across:

Basically you need to remove the computer from the domain and then re-connect to the domain but you may get temporary profile login and you may want to restore your old profile(s).

Logon to the computer as a local administrator (not the domain administrator).  This will ensure you have the correct account details to log into the computer when it is removed from the domain.

Click on Start button -> Right click on Computer -> Select Properties -> Click on the Advanced System Settings link -> Click on the Computer Name TAB.

Click on the Change button (make a note of the domain name, you should already know it), select Workgroup and enter a workgroup name (it doesn’t matter what).  Click on OK and enter the administrator username and password to allow you to leave the domain.  You will have to restart the computer.

Make sure you are connected to the network and login as the local administrator.

Click Start button -> Computer -> Open Local disk C: -> Open Users

Rename the profile name of the user that uses the computer.  For example if the Username that logged into the domain was JoeBloggs you would see a folder called JoeBloggs, rename it to JoeBloggs.OLD.

Connect to domain: Click on Start button -> Right click on Computer -> Select Properties -> Click on the Advanced System Settings link -> Click on the Computer Name TAB.

Click on the Change button, select Domain and type in the domain name (either you know it or you made a note of it earlier).  Click on OK and type in the administrators / admin account username and password to authenticate connection.  Click on OK until you have to restart the computer.

After restart login as the domain user NOTE: If you log in with a temporary profile go to the next step, if you login successfully go to restoring profile step.

You are about to use the registry – if you don’t know what you are doing, don’t do it. Make sure you take a backup of your registry.  Don’t come back to me if YOU break your computer.

Log off and login as local administrator (you may not have to login as local administrator) run regedit and navigate to:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\ProfileList
You will see some profiles listed – go to the longer name strings and highlight the top one.  In the right hand pane look for ProfileImagePath, this will display the path to the Users folder.  Search through the longer name strings until you find the correct profile – in Joe Bloggs case it will read C:\Users\JoeBloggs.  When you find it delete the long name string.

Log off and login as the domain user, this should now login and create a new profile.

Now to restore the user’s profile:
Now restart your computer and login as local administrator.

Click Start button -> Computer -> Open Local disk C: -> Open Users

You will see the users folders.  In my Joe Bloggs example you should see two folders – JoeBloggs and JoeBloggs.OLD.  To restore the profile rename JoeBloggs to JoeBloggs.NOT.NEEDED and then rename JoeBloggs.OLD to JoeBloggs.

Log off and login as the domain user (JoeBloggs) and the profile is restored.

You may have to do the profile backup and restore process for multiple users.