This can be caused by a registry setting named RestrictAnonymous. Go to the computer which you cannot access, start a registry editor and change the following registry value.
HKEY_LOCAL_MACHINE
\SYSTEM
\CurrentControlSet
\Control
\Lsa
Value name: RestrictAnonymous
Value type: DWORD
If the value is 1 or even 2, change it to 0, reboot and retest. If the problem is solved, leave the value at zero. If not, you can change it back if you like.
Check immediately afterwards and again after a reboot, whether the value changes back to non-zero on its own. If that happens, then you have to find the culprit, which can be spyware, a worm, or a badly designed security program. In this case this procedure most likely solved your problem, but then the bad software stepped back in and recreated the problem.