How to verify CPU cooler is dead or ok ?

Problem is after seating the CPU's(is a dual socket board) the board is not beeping and there are no signs or power.

I tested my PSU using ultra 20/24 pin PSU tester it passed, beeped and as well the LEDs are on.

I suspect the CPU cooler, which is rare but the question is how to make sure its working ? can we connect the 3 -pin connector to any of the voltmeter or some stuff (ps newbie to electronics)

Its a brand new board so sparing to suspect on it.

Could be a number of issues, but the CPU cooler has nothing to do with it. As long as it is seated, you're fine. If the fan on it doesn't work you'll get an error message, but the mobo will power up and post normally. Unfortunately, in many cases such as this it is the motherboard that is at fault. Is the power switch hooked up correctly? It seems simple, but this can cause problems even for pros. Is the power switch functional? Use an ohmmeter and make sure resistance between the leads drops off to nothing when the switch is depressed. Is RAM installed? Do you have your system speaker hooked up? What model is the motherboard? And the PSU?

No, it's likely the motherboard that is faulty. I can't see getting 2 CPU's that are faulty. Even with a bad CPU the computer will usually give a beep code and at least power up momentarily. RMA your motherboard.