Flashing boxes on screen
Regardless of what the satellite company says, I would find a way to try another satellite reciever to start with. I have seen this from cable boxes and satellite recievers many times. I have also seen this with a bad LNB, distribution amplifier, or a bad active splitter, or a bad cable, or a bad connector.
There is a data loss somewhere, and the set is seeing what we call aliasing. This is a loss of data, and it shows as blocks.
It is possible for your set have internal aliasing if there is a fault on one of the processor boards. The only way you will easily know if the problem is external or internal to the set is to try another source.
From your description, if other sources work with the set, then this strongly rules out the set. To easily know if the fault is on the input that the sat reciever uses, if possible swap the position with the DVD player.
On the sat system, a defect in the reciever, the LNB, or any LNB splitters or a relay, or a bad connector, can also cause aliasing because of a signal loss.
Jerry G.