Hi All,
I was having this problem, and in my case the culprit was in the file:
catalog/checkout_shipping.php.
This line appeared twice in my page, once near the top and then again in the body:
$quotes = $shipping_modules->quote();
I had this line added into the body due to the Multiple Vendor Shipping (MVS) module that I installed some time ago. I removed the entry at the top, because the one in the body was part of MVS and it fixed the issue.
So, check for the line, $quotes = $shipping_modules->quote(); and make sure it only appears once.
Good luck!