Dell Precision 5520 Windows 10 Prof. will not boot without the power adaptor even when the battery is fully charged, I also replaced the battery and same thing. Once I powered up using the power adaptor I can unplug the power adaptor and run just fine off the battery. But if I restart the laptop it will not power up until I plug in the power adaptor
Have you looked in the BIOS whether there are any settings there that could cause this?
Have you checked whether there is a BIOS upgrade available?
I updated to the latest BIOS upgrade
the power button acts like it is set to "Do nothing" if pressed when I do not have the power adaptor plugged int
remove Ac adapter and battery
hold power button for 10 sec
now reconnect and test power up
Some models of Dell(& HP) laptops look for a battery identifier at boot and will not boot if it is not recognised.
There could also be something off with the battery's output that the laptop doesn't like