Replace action="" with action=""
Not sure if the site search stuff would work, but name="site" might work for the site search part of the code.
<div class="panel bg3">
  <div class="inner">
    <span class="corners-top"><span></span></span>
   <h3>Duckduckgo Search query</h3>
        <dt><label for="q">ddg Site Search:</label><br><span>To search a phrase, surround in double quotes ""<br/> To exclude terms, lead with -<br/>  For exact terms, lead with +<br/>For wildcards use * </span></dt>
          <form method="get" action="">
            <input type="text" name="q" size="40" maxlength="255" value="" class="inputbox"/><br/>
            <input type="radio" name="site" value="" checked="checked" /> Forums Only <br/>
            <input type="radio" name="site" value="" /> Entire Site<br/>
            <input type="submit" value="Duckduckgo Search" />
  <span class="corners-bottom"><span></span></span>

No idea if that code will work in practice, but it should
posted by [Old Forum atomic1fire] • 6 years and 8 months ago Link