Just had the same problem after installing an SSD. Make sure that the power button cable is not severed. Mine was.
Once I took the two button cables and connected them, it turned right on.
In order to fix it, you’ll have to push the physical button out of the back casing.
NOTE - It looks like you have to unscrew the button from the frame (which looks impossible, and is), so don’t try to do that. It is only held in by some pretty strong glue, so take your time, but it will just push and wiggle out.
Once you have it out, there are 3 screws as a guard for the circuit. Take those out and you will have access to the leads, which you will need to re-solder the cables to.
* Be careful when removing the broken wires from the leads!! ***
I almost tore one of them off very easily, so be patient.
Once done, screw the circuit guard back onto the frame of the button. I superglued the cables to the hole where the frame that it comes out of, but don’t do that if you worry.
Once screwed back together, test it to make sure that you fixed it. If it works, you can wiggle it back into the casing and reassemble the machine.
Stupid mistake, but took me 3 days to consider that as my mistake. This is so you won’t be plagued for as long.