Enter the email section from the Home menu and add an external email address (Yahoo, Gmail, Hotmail, etc) to your Wii address book. From the Wii, send yourself a new message to that same email address. After you receive the new message on your computer email account (can sometimes take an hour), reply back to your Wii email account. After a few minutes, you will have a new message waiting in your Wii inbox. As long as you don’t read the message and it remains new, the Wii will light up blue indicating the new message!
The only downside of this process is that the blue light will stay constantly lit even if the Wii is turned off. I would imagine, however, that you won’t have to worry about the LED burning out anytime soon.