If you are encountering a 10002 error from your PrestaShop Paypal module, the reason that you are getting it is pretty simple. It means that your API information you entered is incorrect. To fix it try to copy the API information over again and test to see if it works. If that does not work, you need to try to hand type the API information, because sometimes copying will pick up extra whitespace that will break things.
You can find a full list of the Paypal API error codes here if you are experiencing a different error message.