php while mysql_fetch_array inside while

After the first iteration of the first loop, the internal pointer of the second result set is at the end, so the second loop will not execute, because mysql_fetch_array() will return false immediately. If you want to it exactly as above - the second result set is not dependant on the first - you will need to do this:

// First, get the results of set 2 into an array
$resultset2 = array();
while ($row = mysql_fetch_assoc($result2)) $resultset2[] = $row;

while ($row = mysql_fetch_assoc($result)) { // Do your thang
  echo "<li class=\"s01\"><a class=\"s03\" href=" . $row['link'] . "><span>".$row['onomaselidas'] ."</span></a>\n";
  echo "<ul class=\"pn2\">\n";
  $idd[] = $row['idwebsiteprimary'];
  foreach ($resultset2 as $row2) { // Foreach sets it's pointer to the beginning every time, so this should work
    echo "test";
    if ($idd[$url]==$row2['idwebsite']) {
      echo "<li class=\"s01\"><a href=\"a\"><span>". $row2['name'] ."</span></a></li>\n";
    }
  }
  echo "</ul>\n";
}

Alternatively, you can reset the internal pointer of $result2 on each iteration of the first loop by calling mysql_data_seek($result2, 0); like this:

while ($row = mysql_fetch_array($result)) {
  echo "<li class=\"s01\"><a class=\"s03\" href=" . $row['link'] . "><span>". $row['onomaselidas'] ."</span></a>\n";
  echo "<ul class=\"pn2\">\n";
  $idd[] = $row['idwebsiteprimary'];
  mysql_data_seek($result2, 0);
  while ($row2 = mysql_fetch_array($result2)) {
    echo "test";
    if($idd[$url]==$row2['idwebsite']) {
      echo "<li class=\"s01\"><a href=\"a\"><span>". $row2['name'] ."</span></a></li>\n";
    }
  }
  echo "</ul>\n";
}