At 9 days old, bring it back and get it exchanged or return it. If they won't help you, then never buy from there again, and contact ZTE regarding a warranty claim and they will replace it. You shouldn't have to pay for something that couldn't even last 9 days. ZTE should have a 1 year warranty on it.

If I had to take a shot in the dark, I'd wager its a bad hard drive. Try booting to a linux OS, or use something like Hiren's BootCD or PartedMagic. You can see if it at least boots up with those, then you'll know that its a Software (windows) problem or the HDD. You'll also be able to test the HDD in Hiren's or PartedMagic to confirm its ok/bad. If you're feeling adventurous and your other laptop has Windows 10 installed, you could also swap its own hard drive into the troublesome one. Windows 10 is pretty good at booting even if its suddenly in a totally different PC. Just make sure you back up your data, just in case any settings get screwy after it re-configures (not common, but always a chance). If it boots up ok, then its pretty likely to just be the OS or HDD.

The most common causes are: 1) The AC Adapter (charger) died, and isn't providing any power. 2) The DC Jack (the port where you plug the charger into the laptop) is damaged and not properly connected to the motherboard anymore. 3) The motherboard suffered a component level failure 4) The battery suffered a failure and is causing a short. Basically what I'd try first is unplugging the battery, then plug in the charger and see if the computer works with the battery not in it. Then I'd try a new charger. After that I'd crack open the computer and see if DC Jack is soldered on and possibly broken, or if its a harness type then just unplug it and plug it back in. You can use a multimeter to see if power is getting through the jack too.

Minho is on the right track. I would expect that there's just a lot of "pocket lint" or similar gunk stuffing up the port and the charging cable simply isn't making contact. I'd recommend you take a wooden toothpick or something similar and just see if you can scrape any gunk out of the port. I work at a repair shop, and almost always this is the only problem when people mention a poor fit with the cable and no-power issues. Its much more rare for the port itself to be damaged.

Of those dozens of chargers and cables, were any of them rated at higher than .5A? Remember that a cheap cable will limit how much current can be drawn even from a good charger. I'd say find a brand name (Samsung for instance) charger rated at 2amps and use that charger with the cable that came with it. Or find a brand name Quick Charge 3.0 charger that comes with its own cable and use that. Other possibilities could be logic board issues (liquid damage, or even a manufacturing defect that finally showed up), or the battery itself.

Looks like its a 0 ohm 0402 resistor.

Does the camera and proximity sensor still work? Does it still have the plastic bracket around the ambient light sensor? If the plastic bracket is missing, that can often cause this issue, especially if its happening with multiple flex cables. You should have both the clear plastic pieces circled in this pic. If you don't then they probably lost them and didn't think it was important due to inexperience / laziness. http://i.imgur.com/h4CEFcq.jpg

If you have someone call your phone, does it still vibrate/ring? Or does your computer recognize it when you plug it in through USB? If so, then you'll probably just need to replace the screen assembly. Find an LCD/Digitizer assembly for the 5S, iFixit sells good quality ones (the cheap ones can cause major problems and in my opinion are a waste of money). I doubt the power outage caused it, as it sounds like the LCD is damaged. Black lines and splotches are typical of a physically damaged LCD.

I doubt its the GPU, thats not as common as the internet likes to think it is. If you have another Mac, I'd recommend installing MacOS on a USB drive and see if you can boot off of that. From there, hopefully you can use the external monitor to recover your data. Then you could create a MacOS installer USB to try to reformat the SSD and reinstall MacOS. This probably won't solve your display issue though, only the failure to boot that you're seeing with the external monitor. You may have two faults, the first being the LCD which is why Apple said to get it replaced, but possibly also the operating system may have become corrupted. If you've been turning it off and on over and over while its trying to boot, you may have accidentally corrupted it while trying to figure out the no display issue (computers don't like to be interrupted while trying to boot). Unfortunately, this is probably a good situation to either bring it to the Apple Store or a local repair shop who has parts on hand to test the various...

Is the computer turning on when its plugged in to the wall? If not, take the battery out of the laptop, and see if it turns on while plugged in with no battery. If it still doesn't work, then it could be your charger is bad, or it will be a problem with the charging port on the laptop, or a problem with the motherboard. A dead battery shouldn't stop the computer from turning on unless its also causing a short circuit which is not very common. If you brought this into my shop, the first thing I would do is test a new charger. If you don't have one, see if there's a local computer repair shop nearby where they can plug in one of their chargers for you.