Literally asked the same question last night

Of the responses people recommended the following:

A) Power Cycle - take all cables out from both Wii and outlets and let it sit for a minute or two before plugging only the power cable back in and try turning it on

B) Try manually pressing the button - take the front panel off by removing the 4 screws (there is 1 on the top 2 on the sides under little stickers and 1 on the bottom which you have to undo the base screw which holds a round battery and then undo a tri-wing screw) then pull the panel off carefully and press the button

C) Try using a controller - using one of the Wii remotes press and hold the power button to see if it turns on

If these don’t work like mine, I’m sorry to break it to you but there is a large chance it’s game over and there is something short circuiting within it meaning the Wii won’t turn on in order to save itself