Steps to reproduce:
1. Enable the module.
2. Enter the module settings.

Now login button does not appear anywhere.

Reason:
/**
* Implements hook_form_alter().
*/
function friendconnect_form_comment_form_alter(&$form, $form_state) {
global $user;

friendconnect_add_gadget('login');

$form['friendconnect'] = array(
'#type' => 'fieldset',
'#title' => t('Google Friend Connect (leave a quick comment)'),
'#weight' => -1,
'#access' => !$user->uid && variable_get('friendconnect_siteid', ''),
);
$form['friendconnect']['friendconnect_display'] = array(
'#type' => 'markup',
'#prefix' => '

',
'#value' => t('Loading'),
'#suffix' => '

',
);
}

there is no such hook....

Solution:

/**
* Implements hook_form_alter().
*/
//function friendconnect_form_comment_form_alter(&$form, $form_state) {
function friendconnect_form_alter(&$form, $form_state, $form_id) {
global $user;
if ($form_id == 'user_login_block' || $form_id == 'user_login') {
friendconnect_add_gadget('login');
$form['friendconnect']['friendconnect_display'] = array(
'#type' => 'markup',
'#prefix' => '

',
'#value' => t('Loading'),
'#suffix' => '

',
);
}
}

and now render $form['friendconnect']['friendconnect_display'] in your corresponding tpl.