uslaw:
Ouch....
Sounds like the dreaded "dead trigger" issue....
Since you just bought it, a return probably would be in order. S&W's CS should be able to take care of you.
However, if you're impatient, and think you can handle the job, follow Apex's or Burwell's instructions to remove the sear block and the sear itself. Clean and lubricate the sear, spring, and plunger.
Be careful - when removing the sear block, the sear pin can get lost, as can the ejector (in some models), and when removing the sear itself, the little spring and plunger under it tend to go flying....
Before you try to get the sear and sear block out of the gun, though, have a look at the trigger bar. Is it bent? There's a "U"-shaped loop at the sear end that should be fairly tight, and the remaining straight portion should be straight.... Also, see if the sear works with the slide off the gun. With the slide off, and "muzzle" end pointing away from you, pull the trigger bar gently to the right. The sear should pop up - the rear of the sear should stick up in the air a few thousandths - visibly proud.... When you let the trigger bar return to it's normal location, operate the trigger. The sear should drop to nearly flush with the rest of the block. Try this a few times. If it still works reliably, you could still have the dead trigger, but I think I'd put things back together and let S&W work on it unless you're into flying springs

.... (This test should eliminate crud & lubrication issues.) If you're really a glutton for punishment, disassemble the entire sear block and throw everything into an ultrasonic cleaner. Lubricate things later - just about everything should get a coat of something really light, with the various "joints" (like the sear pin) a bit wetter.
You
may have the "MA-Compliant" sear spring and plunger in your new gun. Supposedly S&W started slipstreaming (i.e., no publicity) those into new production in October, but they're also apparently using up old stock and only updating guns where a problem is noted.
(There's really no way to tell which one you have without taking the sear out, unless you're in Massachusetts.... If I understand correctly, every M&P sold there has to have it. This gives a very heavy trigger, but the Burwell or Apex mods will fix that.)
It's also possible that the drop safety plunger (that's the round thing that Burwell and Apex round off/replace in the slide) is not working. You can check that easily from the underside of the slide. The striker should easily move forward about a quarter inch when the plunger is depressed, and that should take almost no pressure on the plunger.
If you can get the striker out, you might want to be sure that it's clean and lubricated, as is the tube. Disassembly is about the same as the Glock. A stuck striker can also cause some of these problems.
I don't claim to be a competent gunsmith - just good enough to get the grips back on a 1911 on the right sides

- but I remember a lot of what I see here, and type fast....
Some of this may be useful. My vote is "just dirty" for a new gun.
Regards,