If you do not have the 12VDC, then you will have to open up the PSU (which uses special screws and may require some "special" attention) and check for continuity (ohms) across the two pins (on the underside of the PCB) on the fuse to see if it is blown or not. The fuse is a black rectangular object located at the incoming (cord that plugs into wall) end of the PSU. If it shows no continuity than you will have to unsolder and replace the fuse. Needless to say, make sure the PSU is not plugged in when you do this.
Although I do not recommend this, I have known people that have just soldered a jumper wire across the two points. This of course bypasses any protection... and posses great risk to further damage to the Wii or your personal health. The fuse is there for a reason, and blew for a reason.