If you have a Galaxy S4 and you face this no Internet issue in spite of connected to the Wi-Fi then no need to worry as this is a common problem, and it happens due to various reasons. I am explaining all the reasons so that you can easily solve the Galaxy S4 connected to Wi-Fi but no Internet issue.
Reasons and solutions to fix Galaxy S4 connected to Wi-Fi but no internet issue
When you try to connect to the Wi-Fi, a password is required to enter. Make sure that you have put the correct password in order to access the Internet connection.
Enabled Airplane mode
Sometimes it may happen that you have enabled the Airplane Mode and forgot to disable it. Few problems occur in android phones when the Airplane mode is kept on. So it is advisable to check and disable in case the Airplane mode is ON.
Lots of devices connected to Wi-Fi
When so many devices remain connected to the same Wi-Fi network then it might be difficult for one device to get the available network. So disconnect few devices that are connected to Wi-Fi and then see if the problem is solved.
Incorrect DNS Settings
Incorrect DNS setting is one of the main reasons behind this problem. So you need to change the settings by the following way.
Go to the Settings > More > VPN > Edit profile > Show advanced option and some options will be appeared. Enter the DNS server there. You can enter here 220.127.116.11.18.104.22.168 or 22.214.171.124 and click ‘save’. Now your phone will use this DNS server while connecting with the VPN profile.
So trying all the above method one by one will help you to fix Galaxy S4 connected to Wi-Fi but no Internet issue, and you can easily have access to the Internet.