New
#21
The Original symptoms sound very similar to a Gateway NV53 I have recently fixed for a Friend ....sort of..... , my friend had given up on it and brought a new one....but it was actually a Bad motherboard (solder I beleive) and if you let the computer Sleep or turn it off and let it cool down , it was very difficult to get re-started and you'd just see the black screen you mentioned. Wouldn't surprise me if yours is similar being a refurb.
It initial "fix" was to wrap it in a Bath towel once at the black screen and leave it for 30-45mins till it got extra hot and then restart it and it would boot every time , now it is setup to never sleep ( just screen off ) or hibernate and must be always left plugged in, so the MB stays warm , just this week it upgraded to 1803 without issues too.