I added a separate HTML gadget and typed in the code from the following site to create my "Search This Blog". At the moment, the Search button is below the input box. That doesn't look good - but it works. I have been surfing to find out how to move it up to the right. I'll fix that sometime.
Then I edited the Google Search gadget to just search the Internet and Links by unclicking the radio button for Search This Blog. I might retry that feature on the Google Search gadget now & then after some time passes. I found this thread - "Search this blog not working" - on the Blogger Help, so some other users have had trouble with this Google gadget not searching their blogs.