XPS 13 9350 won't start; power button flashes; battery level indicator also flashes

My XPS 13 won't start. I followed all the suggestions I found on line. I disconnected the main battery and the CMOS battery, disconnected the power adapter as well, and kept pressing the power button for more than 15 seconds. After that I connected the batteries and tried again. With our without the power cable, the only thing that happened was that the power button flashed repeatedly, and the battery-level indicator on the left side of the laptop also flashed repeatedly. I tried to start the laptop by hitting the power button with no success. (No light comes on on the front side. No light on the screen either, needless to say.) 

I replaced the main battery and the CMOS battery, and I also used a new power adapter cable. That did not change a thing. I had the flighting lights on the power button and the battery-level indicator (without touching). After about 15 minutes, I am not even getting the flashing lights either. I see no sign of life on this machine.

Does this mean that the motherboard is faulty? Any other possible issue? Any help is greatly appreciated.

(When my son was using it, the computer suddenly turned itself off. When he restarted the machine, it worked fine. This type of issue occurred a couple of times, and then it completely stopped working, according to his report.)

9350-1340SLV Core i5 128GB Signature Edition Laptop. It is almost 6 years old. (The main battery was only about 1.5 years old (before the replacement).