The Wii red light means that the console is completely off, whereas a yellow light would indicate standby mode. From a quick [link|http://answers.yahoo.com/question/index?qid=20071026143203AAxRBRb|internet] search:
''Green light = Console power is on''
''Orange/yellow = Wiiconnect24 is on''
''Red = Wiiconnect24 is off''
''Wiiconnect24 is where your wii recieves data via wifi or lan while your console is on standby. ''
Your problem with the Wii powering on has nothing to do with the red light -- it's not like the Red Ring of Death on the Xbox 360...
The blue disc light should flash like it does. Try to [[Nintendo Wii Troubleshooting|troubleshoot the Wii]] and update your original post with more information if you can.