sounds like it's over heating..do you hear the fan running? can you feel a breeze from console? does it feel unusually warm? It might benefit from opening the case and a thorough dusting of fans and visible parts. Static really attracts dust in our machines...you vacuum the house more often than we clear out dust from these things. try it and see. the guide for opening your console is linked under the photo of the wii on the right.
It might be a short in the system because you cleaned it, or a dead power supply
A friend was having issues with power, I told him to buy a power supply from gamestop and it was fixed
If it still does this with a new power supply, take it apart and see if any capacitors are bulging in it, this might be why
If the caps are fine, motherboard may have shorted somehow and now the motherboard is dead