It turned out that this Dell series don't support G.Skill ram sticks. I've ordered new ones made by Crucial and it worked perfectly! 
I've decided to upgrade my RAM from 16GB to 32GB so I bought the G.Skill one (F4-2400C16D-32GRS). It has the same type, voltage, and speed as the previous sticks (SO-DIMM, DDR4, 2400MHz, 1.2V). I also made sure that this laptop model can handle more RAM. I unplugged a battery for ~10min, replaced RAM sticks, plugged the battery back, and then powered on. At first, there was a white screen "Alert! The amount of system memory has changed" with the button "Continue" and "Open BIOS". I opened BIOS (which was the Dell UEFI menu in fact) and there was nothing more to do than just checking if the system sees a new memory correctly and everything seemed ok there so I left this menu.  The laptop started to boot, it showed the Dell logo, then the Windows 10 login screen and the screen goes all black. I tried switching and re-installing the RAM sticks over and over but with no result.  Everything goes back to normal if I switch to the old RAM. What could be a reason that it won't run with the new one? 
System boots, Windows 10 not (black screen) after RAM upgrade in Precision 5510