Why are my radio buttons not displaying?
Form builder functions must return a form array, not a string, otherwise they won't work with drupal_get_form(). If you need to add markup before and after the form you you should use the #prefix and #suffix properties, or do it outside of the form function altogether.

Also the function signature for Drupal 6 should not contain the $form variable as an argument, but the $form_state variable instead. And you're currently setting the value (text) of the submit button to the HTML representation of a an &lt;input&gt; field which will never do what you want.

Try using code like this instead:

function ismiv3point1_search_block_form($form_state) {
  $form['search_block_form']['#title'] = ''; 
  $form['search_block_form']['#value'] = 'Search mysite.org';

  $form['submit']['#type'] = 'markup'; 
  $form['submit']['#value'] = 'Search the Site';
  $form['submit']['#weight'] = 2;


  // this is the new field I'm trying to add  
  $form['image_switch'] = array(
      '#type' =&gt; 'radios',
      '#title' =&gt; t('Image Switch Radios'),
      '#prefix' =&gt; '&lt;br /&gt;&lt;span style="color:#fff"&gt;',
      '#suffix'   =&gt; '&lt;/span&gt;',
      '#weight' =&gt; '3',
      '#options' =&gt; array(
          1 =&gt; t('Images'),
          2 =&gt; t('All'),
      ),  
      '#default_value' =&gt; 1       
  );

  $form['#prefix'] = '&lt;div id="search-box" style="margin-top: 10px; margin-bottom: 0px;"&gt;';
  $form['#suffix'] = '
      &lt;div id="search-loading"&gt;&lt;/div&gt;
      &lt;div id="current-type"&gt;&lt;a href="#" class="date"&gt;Sort by newest first&lt;/a&gt;&lt;/div&gt;
      &lt;ul class="content-types"&gt;
          &lt;li&gt;&lt;a href="#" class="date"&gt;Sort by newest first&lt;/a&gt;&lt;/li&gt;
          &lt;li&gt;&lt;a href="#" class="relevance"&gt;Sort by relevance&lt;/a&gt;&lt;/li&gt;
      &lt;/ul&gt;
  &lt;/div&gt;';

  return $form;
}


EDIT

Just a bit of extra info on how to do this with a form alter hook:

function ismiv3point1_form_search_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  $form['image_switch'] = array(
    '#type' =&gt; 'radios',
    '#title' =&gt; t('Image Switch Radios'),
    '#prefix' =&gt; '&lt;br /&gt;&lt;span style="color:#fff"&gt;',
    '#suffix'   =&gt; '&lt;/span&gt;',
    '#weight' =&gt; '3',
    '#options' =&gt; array(
        1 =&gt; t('Images'),
        2 =&gt; t('All'),
    ),  
    '#default_value' =&gt; 1       
  );
}