Checkout Error – Call to Undefined Function mcrypt_module_open() in Magento

Mage_Directory_Helper_Data::getRegionJsonByStore() was introduced in Magento 1.8, so it sounds like your Mage_Directory_Helper_Data class is from an older version.

The most likely explanation is an override in app/code/local. You did not explain how you "disabled app/local" but it probably didn't work.

Can you please open lib/Zend/Uri/Http.php file and add the following lines:

$a = $this->validateUsername();
$b = $this->validatePassword();
$c = $this->validateHost();
$d = $this->validatePort();
$e = $this->validatePath();
$f = $this->validateQuery();
$g =  $this->validateFragment();
var_dump($a, $b, $c, $d, $e, $f, $g);
exit;

above the

// Validate the URI
if ($this->valid() === false) {

And post the output here. This way we can check what part of the url can't pass validation.

Also, could you please tell what the values are for "web/unsecure/base_url" and "web/secure/base_url" in your core_config_data table?