1. First thing to try is resetting the BIOS. And do a hard reset while waiting 5-10 minutes (remove battery and power cable and press power button for a minute)
2. If the PSU seems good, and at least the case fan and HDD run, the PSU may not be supplying the necessary wattage... Running fans mean nothing, just that they use less power than the motherboard.
a) Check power connections are snug and fully seated.
b) Try a different PSU.
3. If case fan and HDD run with a known good PSU, but not the motherboard; two possible causes: Dead BIOS chip or dead motherboard.
4. CPU is unlikely to have died specially if the issue happened without warning or apparent cause.
I had one mobo that died like this and I've read other cases where the mobo died the same way. If the mobo doesn't have signs of damage, you can try recovering the BIOS with an update if you learn the update keys and procedure to do it blind, if still nothing, replacing the BIOS chip would be recommended where possible, if done and still nothing, it's time to replace the motherboard.
Recap:
1. Reset the BIOS to remove any corrupt settings.
2. Make sure it's not the PSU or lose/defficient power connection
3. If possible update the BIOS, next up replace the BIOS chip... and next up replace the motherboard.
4. CPUs don't die without a good reason: mainly overheating or shortcircuiting