In my case it was the CMOS battery… Replaced it, now it works.
The test is simple.
Remove battery, disconnect power source, remove back cover (gives access to HDD, RAM, etc) and *carefully * remove the coin like battery (there's visual tutorials for this on YouTube).
Without the battery, turn it on. You should hear the fans and HDD spinning up. Let go of the power button and press again to force shutdown.
I had to get a Duracell CR 2032 (Pharmacies and small stores have them) and replace it.
That's it.
Hope this helps.
Start saving up for the next PC (parts for this have been discontinued for a while now).
Cheers!