Battery not charging at only 35 cycles - recoverable?
The battery is showing at 35 cycles but not holding any charge whatsoever. I presume it's been sat on a shelf for some period of time and has drained, but I can't imagine that it's actually dead at only 35 cycles.


There's a number of things that can be at play here:


Bad charging circuitry.  The battery is actually good, but power isn't getting to the battery itself.
A defective battery.  It happens; these are "man-made" items and far from perfect.  


Won't charge at all
Won't hold a charge.  Charges but dissipates quickly (as you describe).  This is due to a bad cell.
Reduced charging capacity

Wrong charger.  It's entirely possible you got a charger with too low a wattage rating.  


Given that you've stated it won't hold a charge, it's likely a defective battery.  Pretty much the only thing you can do is reset the SMC.  The NVRAM has nothing to do with power issues and reinstalling macOS should only be used as a last resort.

However since this is a new purchase, your best option is to return it rather than try to fix it.  It came to you with an issue - the seller should deal with it and it doesn't speak highly to their quality controls.  Don't be discourage that you can't fix it, because, technically, you can:  replace the battery.  It's just that (IMO) you shouldn't have to unless it was listed as having this condition.