My Wii has a red light on the front to say it is switched off.
Now when i press the power button to start it up the blue light around the cd hole turns blue. This happends at the time I press the button, as soon as I release the button the power light turns red again.
I've had a look on the net to see if there is a soultion to your problem and found this bit of info which may help.
.."push the reset button and if that doesn't work unplug all cords and memory cards (including sd) from wii and unplug av from the wii and the outlet in wall. Wait 2-3 min and then plug it back in..."