Where can I download just the Google Desktop Search component of Google Desktop, without the sidebar, etc.?

Answer 1

If the older versions didn't have the sidebar then you could try by downloading one of those from here:
http://www.oldapps.com/download_google_desktop.php

If you just don't like the sidebar - I sure don't - you can always close it and that way it shouldn't bother you. You can minimize it by clicking on the down-arrow in the upper right corner.

Answer 2

you cant