First off, why is this tagged PO? But when you say switched, do you mean turned it off? Well, if it shows red it has nothing to do with Dream world. Let me explain.
It will be red on your C-Gear when you aren't in the range of other Dsis, or aren't connecting with them. Stuff like that. Not wi-fi, but wireless communications.
You can't access Dream World when you have no Wi-Fi. If you can't access dream world, that doesn't mean the light is red, only that your wireless communications aren't up. Or maybe your communications are disabled.
How to turn wireless communication on or off:
On the Nintendo DSi Menu, use the stylus to select the Settings ("wrench") icon.
Select "Wireless Communication Settings," then select the desired setting ("On" or "Off").
Select "OK" to save the changes.