The parts most likely to be DOA or defective are, the video card, motherboard, HDD and the Ram. How ever in the 12+ years I have been ordering parts/building PC's I have yet to get one that didn't work, or that was DOA/defective, so the chances are very slim. You also need to note that PC parts are built on a Massive scale so expect defects here an there, which are rare in them self's .
I've had a dead refurbished GTX470, spent hours before I finally believed that it was DOA. I had one I could compare it to, and the replacement was fine. Other than that out of maybe 50-60 other components i've ordered over 10 years there has been nothing.