Vostro 3500 shuts down, can't restart

Hello everyone!

I bought second hand this laptop with symptom "Dead, doesn't boot", so can't tell a lot about its story.

The thing is it shuts down randomly, nor a temperature, neither a battery charge level issue, it's really random. I upgraded it to the latest firmware last week (?) through bios update assistant, no errors. I ran full system test a couple of times, no error. S3, I think, was switched off all the times, the same about secure platform. The only way to wake it up, is to disconnect the main battery for a few minutes and press a couple of times the power button. One thing is sure, every time this happens the power led on the side doesn't turn on when I connect the power supply.

One last thing, most times the clock is reset but can't recall if I get the usual CMOS error every time mainly because I press the F12 button. I changed the backup battery and checked for voltage presence on the other side of the flat ribbon cable, everything looks fine.

I hope all these make a sense to you.

Thank you in advance!

Lefteris