I would open the doors to all the drives. Then with the power cord detached, cycle the button a few times to make sure it is solidly clicking into the on position and then clicking back out into the off position.
Attach power cord and power on - no drives are attached, but fans (12 volt) and LED lights (5 volt) will tell us if the power supply is providing power.
Next, one at a time, close each drive door and observe on Disk Utility whether the drive is mounting. If it is, then dismount it and open its door and try the next one.
Essentially - we want to prove we have power. Then we want to test each drive to make sure one of them isn't the source of the problem.
Depending on your results we can continue on with other testing and determine a fix.
"I am a mortal enemy to arbitrary government and unlimited power. I am naturally very jealous for the rights and liberties of my country, and the least encroachment of those invaluable privileges is apt to make my blood boil."