Bad caps shorting in a supply can easily cook a board. but the description of immediate shotdowns when first starting up the system with only fans running and no posting is most one or caps on the board itself. On a new bui;d here the 2-3seconds seen would see the blue leds on the fans as those spun for those few seconds and then everything goes dark.
A bad cpu on the other hand would most likely result in you hearing a constant beeping from the speaker on the board if nothing visual appeard onscreen. With no audio alerts the board becomes the main thing there. Those codes include bad ram along with having a bad video card as another hardware. If you haven't been hearing the single beep when first starting the system the fault is on the board.