Dell latitude E6440 randomly not starting

Hi All! I have an old Delll E6440, which started acting weird 1 month ago. After any kind of swiching it off (includes shutdown, hibernation, sleep), randomly i can't wake it up (this can happen even on restart), when i press the power button these can happen:

• the power LED on, and that's all. Nothing happens, the HDD, or battery charging LED does nothing, the screen is off, i can't turn it off, even if i press the power button for 10 seconds, i can only turn off by removing the battery
• power led on, some blinking of hdd led, but then same as above
• power led on, hdd led blinking, dell logo comes up on screen, hangs there, others are same as above
• starts correctly, and i can use, but its very slow, like if the CPU is running at low frequency, also on linux mint (main os) this time the battery indicator is missing, like if it would be a desktop pc, the system not even detects the battery, or charging, even if it runs from battery only. After a half hour, the cooler revs up, the system gets faster, like normally, and the battery/charging indicator appears
• starts correctly, everything is normal, and stable

So a usually turn on, is like this: fail, take out battery and back, fail, battery out-in, fail, battery..., starts correctly. But for example today i had to to the battery cycle 8 times until it started.

I've checked the cmos battery, its fine with voltage a little bit above the nominal, and never was UEFI settings loss. I've tried without the HDD(SSD) too, nothing changed.

I've tried to start without battery, on charger, but no any reaction on power button, not even the LED. The charger supplies the normal voltage, also tried with other charger for same type, but nothing changed. If the laptop starts correctly, also charges the battery as normal.

Do anyone have some hints, why is this happening? I've done longer RAM tests too, no error.