My iphone says it's connected to a Wi-Fi network when it really isn't?

When I go to the settings page, my phone says it's connected to a Wi-Fi network, but the little 4g symbol at the top stays the same.

You must click again on your Wi-Fi network when the Wi-Fi symbol become blue at the bottom and if it doesn't work, you'll have to reset your iPhone or change it in an Apple store.
You're lucky to have 4G… In France we just have 3G+ or H+.

It might have mattered to say what Wi-Fi network you're connected to. The iPod/iphone picks up Wi-Fi networks which aren't Wi-Fi networks that get you on the internet - like the wireless connections for printers. You may have also connected to a network you don't have access privileges to. Your question says nothing about this at all.

For anyone who has this problem and has done everything possible to get connected. These things include resetting your network, checking your router, turning Wi-Fi on and off, forgetting the network, rebooting the phone, etc. If all of that fails, try seeing if your date and time are set correctly, I know this sounds kinda stupid but that happened to me and my connection worked as soon as the date and time were correct.