I couldn't get the Google "Search This Blog" widget to work. The "Powered by Google" search box was and still is Broken on my newest blog-
Ironically, I used Google search to determine that this has been a widespread problem off and on since 2009.
The following link provides a workaround fix-
Blogger Search Engine (powered by Google) is not working in my blog! - Blogger Helpuser davidchin38 says-
You can add another search box.
These are the codes:
Go to layout, click on:-
1. "add a gadget" (scroll down to html/javascript)
2. "add to blog" (paste these codes in the large box)
3. save (you can now drag and drop your new search box any where on your page.)
This is working fine for me until Blogger can fix the "Powered by Google" widget.
If you are having the same problem, you can help Google fix it by posting information here-
http://www.google.com/support/forum/p/blogger/thread?tid=219c1929f5d3f57f&hl=en