I feel for you, receiving a faulty projector after waiting for this long is a bummer, no doubt. But good QC doesn’t mean that every unit gets tested, just that a sample big enough passes the quality control. There will inevitably be some faulty units that slip through. I’ve had experiences like yours with other big brand products.
If you are interested, the QC process is explained in more detail in this post: General info about shipment and manufacturing
If you have sent your complaint through the right channels, you will get a working projector in the end.