Why my laptop turns on and off by itself

Hi, hope you can help with my issue

So, my laptop probook 4540s was working perfectly fine until like 2 weeks ago. That day I had an issue when I plugged the AC adapter and the LED that is on top of the ac jack flashed white, the pc turned on but the battery wasnt charging. I looked it up online and solved it by hard reseting by pressing the power button 15 secs without the ac adapter plugged or the battery.

After that I had no problems until 4 days ago.

This time I was using my laptop as usual in the morning and then hibernated it and went to get food, when I came back I tried to turn on the laptop but I couldn't, when I pressed the power button the only thing it did was that the power button light up, the fan sounded like it was spinning at full speed, the screen was pitch black and after 5-10 secs it shut off. If I tried to to hard reset and nothing. The weird thing is if I left the pc alone after several hours and tried to turn it on, it worked properly but if I hibernated it or shut it off the problem appeared again.

I looked online and I saw in forums that it could be

1. The laptop was overheating, that could explain why it shut off by itself and why it worked after leaving it and trying hours after or 2. The BIOS was corrupted and registering a wrong temperature.

So I opened the pc, I dusted it off, removed the heatsink and cleaned it, reapplied thermal paste to the CPU and external graphic card, also I disconnected the CMOS battery for 5 min to reset the BIOS.

I then put the laptop together and to my surprise when I connected the battery or plugged the AC adapter, the pc turned on by itself but now the fan didnt spin, the screen was black, the power button LED lighted on, the HDD led blinked but very dim. Again after 5-10 secs it shut off by itself but instantly turning back on, stuck in a cycle.

One thing I noticed is that the fan was trying to move but it couldnt, like it was also "blinking".

I tried hard reseting but nothing.

I hope I dont messed up any hardware, when I opened the pc up I saw tutorials and were very careful, everything went smooth.

I'll appreciate any help.