Well, first of all, if it is a SAMSUNG monitor (Regardless of you buying it through Dell) your quality complaint is with SAMSUNG.  I can't see how you can hold the failed monitor against Dell.  They can't open the box & test it before it ships.

Have you tried the no signal self-test? Generally if you leave the monitor disconnected, except to its power supply, and turn it on, a test pattern and message will appear. If the monitor does not work, return the monitor ASAP. If it does work then, the PC may have a video problem.