Basically the whole configuration has been changed since a "working config".
- new RAM has been installed: DDR3 Corsair vengeance (2X8GB, CMY8GX3M2A2133C11R)
- a new power supply: 600W, Chieftec
- video card has been changed: installed a GT740 (made by Gigabyte)
What I have tried:
- remove the video card, try to use the integrated one (no luck)
- remove the RAM, see if it beeps to indicate the error (no beep)
- try again with another power supply (also no luck)
What can't be the problem:
- the CPU and the motherboard used to work together, so if there is any incompatibility, it's not there
- no power: the fans are working, and the CPU gets hotter when the CPU fan is removed (for "does the CPU work" testing reasons). "Not enough power" is still an option, but 600W should be enough for this setup
- power not plugged in: both the 24 pin and the 4 pin on the motherboard and the 6 pin on the video card are plugged in
EDIT: Looks like the BIOS got damaged somehow. After correcting that, everything works as expected.