Hi,
I have found your problem and I don't know how you did it. Maybe it's "idealcheckout".
Well, in your hikashop_payment table, you have two "paypal" configuration. Once with "idealcheckoutpaypal" and the other with the real paypal plugin.
The problem is that, the "idealcheckoutpaypal" use the payment_type "PayPal" (and not "paypal")... Because it have a lower id than the real paypal configuration, during the notification, the configuration of the wrong paypal is loaded.
So, the plugin could not work without his configuration. Notification is not processed, etc.
So, I don't know why you have this wrong "PayPal" line but, if you want that the paypal plugin works, you have to delete the wrong entry.
Regards,