I am having basically the same issue, except, I am sure it is NOT permissions. When doing a search from the widget I get the exact issue. It only works when logged in and the widget goes to the page “http://www.mwsolut.com/search_gcse/?q=item searched”. When not not logged in the search from the widget does not work, and it also goes to “http://www.mwsolut.com/search_gcse/?q=item searched”. However doing doing a search from the page “http://www.mwsolut.com/search_gcse/” using the search embedded with in the page content does NOT take me to “http://www.mwsolut.com/search_gcse/?q=item searched”. Instead it takes me to “http://www.mwsolut.com/?s=item+searched”. The URL differs as does the handling of the information placed into the search bar. In the widget does not replace spaces between the words with a “+” between each word entered into the search, but also adds “search_gcse/?q=” to the URL. The search page instead adds “?s=” followed by the words entered into the search bar, but replaces all spaces with “+”. I am leaving the widget in place so you can see the results.
I created a search using custom HTML widget for the WP Google Search and it works fine. I called it “HTML Google Search”, and used the following html:
<form action=”/” method=”get”>
<input type=”text” name=”s”><input type=”submit” value=”Submit”>
This works but the widget from the plugin does not. Go to my site to see what I mean…