The Error 1606, and the NULLDesktop10.0 suggest that a path Environment for your installation account (HKCU) or your system (HKLM) is corrupt. The ArcGIS 10 Desktop program installation goes into C:\Program Files\ArcGIS\Desktop10.0 so the NULL may be the C:\Program Files\ArcGIS which should be setup as the installation package is parsed by the MSIEXEC. Activation and authorization components are dropped into the C:\Program Files\Common Files\ArcGIS\bin folder--so those components are not likely the direct problem.
Note that the paths would be C:\Program Files (x86) for 64-bit Windows 7.
Any chance you are you attempting the installation from an account without Administrators group membership, and are having ACL folder and file write permission issues?
Check these for the account you are trying to install from:
What does echo %APPDATA% entered in a command window return?
What does echo %USERPROFILE%\AppData entered in a command window return?
Have a read of Microsoft KB 886549 here. Check to be sure none of your User Shell Folders are off standard. For the install account, you'd be looking in:
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\User Shell FoldersYou might back up the registry keys, and then try running the 50356 Fix-It linked from the KB 886549 from both your user account and also the Administrator account (from a "Run as Administrator" launched command window) and see if that clears things.
If you verify the User Shell Folders keys are correct, then the next step may be a manual command line installation with verbose logging to see just what is failing during install.
Post back if that is unclear, or if you have any questions.