Windows 2000 logon problem

Is this computer connected to a domain? Do you have the local administrator account and password?
If so try to boot it up into safe mode and log in with the local admin account. If that works then disjoin the computer from the domain and the rejoin it.

I have tried booting up into Safe Mode and logging in as local admin and the same thing happens.

Yes this pc is a member of the domain.

Since it hits the desktop, there might be something in the Startup directory or in the Run key that automatically logs it out. Try holding down the shift key while it logs in (I use the left one, but I don't know if it matters). That should skip the stuff in the startup. Go to another PC, map a drive over to \\COMPUTERNAME\c$ and browse into Documents and Settings, All Users, Start Menu, Programs, Startup and see what's there.
The registry entires are a bit trickier because they can be locked down, but you need to do it remotely, too. Go to another PC, login as the domain admin, run regedit and click on Registry and Connect Network Registry. Enter in \\computer name and it should pull it up. The key would be in HKEYLM\Software\Microsoft\Windows\CurrentVersion\Run and see what is in there. I'd recommend exporting out the that key before you do anything so you can reimport it later if need be.

I also recommend checking the Registry remotely from another machine on your domain.
Look in HKEY_CURRENT_USER\Software\Microsoft\Windows NT\CurrentVersion\Winlogon
Check the value for Shell, to see if it says "explorer.exe" (without the quotes) or if it says something else.

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