Are you using the button on the power control widget? This should work fine, but I'd try using the app drawer button (think that's what it's called) and select the Settings icon then select Wireless & networks. Try to turn on Wi-Fi from there. Essentially there doing the same thing, but maybe doing it via Settings may work.
Once you get it to turn on, you'll be able to add your network.
Maybe try to turn the phone off, and restart it as well. Could be some kind of "glitch".
You may want to try getting an app instead.I have the free app called ToogleWifi by Andrew Schwimmer. It is just one tap of that app and you should connect to wifi right away
The built-in "switch" should work just fine - something weird glitch going on here. Not sure why you'd need to download another app that would take up more storage? I think the Droid OS Power Widget works just fine for most. It includes Wi-Fi, Bluetooth, GPS, Sync and Brightness controls.
I'm guessing something weird is going on here. To the OP: Did you try to reboot the phone?
You didn't indicate why it won't connect, the exact message or whatever. It is pretty simple to do, I don't know why you would need to use an App. I try to avoid additional Apps so they don't use up resources.
Wireless & networks
Set up Wi-Fi network
Add Wi-Fi network (you may be having trouble here if you have security on your home wifi, you need to input the security code, some people lose it) - save the step
Go back to Wi-Fi settings, where you just were
Turn on Wi-Fi
You can also check off if you want to be alerted when a new open network is available -- I prefer a secured network.
The problem I have had is that my phone won't switch between WiFi and 3G mode automatically. I found out when my home wifi went down. I was told by Verizon to shut off my WiFi to use the 3G, etc. I don't understand why that would be necessary (ie., it isn't necessary on the IPhone). I chose to keep WiFi off.