I was getting the "The Local Security Authority cannot be contacted" when connecting from XP to a Windows 7 machine. I had updated the Remote Desktop client software through KB 969084. Don't make this update if you need to access win2000 systems as they are not supported.
I have the firewall turned off for testing purposes, so that wasnt the issue. I applied the CSSP Fix under XP(listed in the KB) and rebooted the XP system, though that may not have been necessary.
It turns out I had almost everything correct.
After reading Osman's solution above, I connected to the remote system though an alternate remote connection method, and added a password to the account.
There should be a note added that the destination account must have a password for RDP to work under Windows 7.
Once the password was added I was able to connect using the Enhanced Security with no errors.