Windows XP logs off right after you login. Safemode will not work either.....same behavior.

Is this a Malware issue?

Taking a guess something deleted or modified the userinit key in the registry.

If you have a BartPE cd or WindowsPE cd you can boot from you can mount the problematic registry and restore the key then scan you machine for malware.

the key is:

HKLM\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Winlogon\userinit

And the value should be (including trailing comma):

C:\windows\system32\userinit.exe,