There's a bug in the current version of PrestaShop which might prevent Remarkety (and anyone else) from accessing the orders via the Web Service.
When installing the Remarkety plugin, we check if this bug exists and alert you to it - here's how to fix it!
In your PrestaShop installation, open the file:
Look for this line (should be around line 2092):
public function getWsCurrentState($state)
and change it to:
public function getWsCurrentState()
Mind that this method is immediately followed by a similar "setter" method named:
public function setWsCurrentState($state)
You only need to modify the "getter" method above.
PS - We've already submitted this patch to PrestaShop and it will be fixed in their next version.