We upgraded to w10 long ago and it was fine.

To force the k55n to not load an OS I would remove the HDD. That way I can be sure nothing of W10 is in play on the laptop.

If you get no display anywhere then it may be an unfortunate coincedence that the laptop failed in some way during or after the upgrade. Our K55N's are from 2012 and one is dead now but from a glass of water. The other is fine.

-> The one with the now bad motherboard does power up, fans go, the DVD drive does a seek but it is really dead.

Given the age you could have many issues but here's what I would try.
1. Remove the HDD so no W10 is in play.
2. Try to get to the BIOS.
3. If you make it to the BIOS disable any Fast Startup item you find then save and power off and put the HDD back in.
4. Use a Volt meter on the CMOS battery. It looks to be the usual CR2032 so you want 3.0V or a bit more there. If you are not a PC tech or such, try a new battery (here, we get them for under 1 buck.)
5. Read https://www.google.com/search?q=k55a+cmos+battery and this link:
https://superuser.com/questions/714353/asus-k55a-black-screen-boot-issue-after-windows-8-1-upgrade

So there are a few things to try before you call it dead and back to repair.