Precision 5530 doesn't want to shut down without power adapter

Hey, everybody! I have a dell 5530. It has a problem: the laptop doesn't want to turn off without the charger plugged in. Also hibernation does not work. 
When I turn off the laptop, it shuts down, then after a couple of seconds it turns back on. But when the charger is connected, the laptop turns off, as soon as I disconnect the charger (on a turned off laptop), it turns on again after a few seconds. I thought that maybe the problem in the drivers, checked and on a clean Windows 10/11 and with drivers. I searched the system for devices that can cause the computer to wake up and found nothing. I even activated the powerdownaftershutdown option in the registry and nothing helps. When the computer shuts down with the power supply, the power LED on the front panel blinks three times after shutdown. 
Now for a related problem: the laptop's power button doesn't work, it physically clicks, the fingerprint scanner cable is connected to the motherboard, but the laptop doesn't respond to the button and the fingerprint scanner doesn't show up in device manager. This may be the problem as well. Since I can't turn on the notebook with the button, I have activated wake-up from the power supply and from the docking station in the bios. Who can advise what?