My problem is still unsolved... According to Tuan - with whom I've had a MSN conversation - it comes from a "communication problem" between Paypal & the component.
I have new information : when I check the database of my website, I see the orders. They appear in the database !!! The problem is that they are not visible in the administration panel of the component & the customer doesn't receive any confirmation/download link.
By the way, it seems I have the same problem with JoomDonation (the donations can be seen in the database but not in the admin panel of the website).
In t0r4j_dms_orders, the field "published" is on 0 for all the orders and the field "payment_date" is "NULL" for all the orders.
Please, I really need some help. I sent my first support ticket on May 2 and I still can't use my component, one month and one week later.