Wii U won't turn on

I remember the PSU of the 3ds has a fuse that self resets after its been out of the power a while. I can imagine the wiiu has a similar system.

 

Most switching power supplies have a capacitor inside of the primary circuit which charges when it's output get shorted out. That causes it to shut down.

It's not a FUSE but it does indeed "reset" after the capacitor discharges.

To have it discharge just remove it from mains and let it sit for a good while (from 15 minutes to one hour).