The only piece of hardware that comes to mind that can shut a system down and leave no trace - PSU.
Get another PSU (beg, borrow or buy one - then return it) and swap it out. Make sure it has enough power for your rig.
The mobo could be involved as well, but I would say to try the PSU swap out first.
Do not disagree just trying to save the cost if not that first, if you had to live on my salery u would understand :)
Regards. . .
jcgriff2