ASRock has over 16 different motherboard models using the z77 chipset. A more descriptive model number could be useful. I imagine it is safe to say that it's not one of the motherboards that feature a power switch and reset button directly on the motherboard or the Debug LED display, as I'm sure you would have noted both of those.
A minimal test for a motherboard would be with only the CPU installed. It should then give a Beep code indicating no RAM, which in this case should be three long beeps. If it doesn't, then it is either a failed CPU or a motherboard problem. as ASRock motherboards will do absolutely nothing (No beeps or anything) without a CPU or with a failed CPU. If it does, then you add back components and attempt to power it up until it fails- which would tend to point you at the last component you added.
It is safe to say there is no visible damage or obviously failed components such as capacitors on the motherboards?
It can also be useful to remove the motherboard from the case (assuming you haven't done so), mostly because it makes it more accessible but also because the issue could be caused by a short with metal components of the case.
One useful feature is the aforementioned "Diagnostic" LED. This is a two-digit, seven segment display that is mounted in many modern motherboards and the Hexadecimal code that it shows effectively tells you what the motherboard is doing. These are an integrated version of a diagnostic tool called a "Diagnostic POST Card", so even without one on the motherboard it is still a possibility. these are expansion cards that can be installed which will effectively monitor the startup process and display a Hex Code. If you have several motherboards that you think have failed it could be useful to get one of those to determine where things are going wrong as it may point you towards possible remedies, or at least give you "Closure" that the board is dead.