I have also had this issue with my Galaxy Tab S3 10.1 running Android 4.2.2, build dated 23 Nov 2013.
The symptoms are -- my Tab S3 WiFi was fine when first set up, but now I can't use the Internet, even though it shows as 'connected'.
Go to Settings (the cog symbol), touch WiFi, and your network -- the first in the list -- shows 'Connected' but doesn't function. Touch this Wi-Fi entry to open a menu and its IP address shows 'unavailable'.
The tablet can't use this Wi-Fi network, as it has lost the IP address.
Possible Cause -- the router will 'lease' an IP address to a device for a while, maybe some days, then forces the device to reconnect when the lease expires. A router restart will also force IP addresses to be re-issued. Our Toshiba and Asus laptops & Nokia and Android phones all cope, but the Tab gets confused and can't reconnect.
I had no issue with wrong time as reported elsewhere on this thread.
The only thing that seemed to fix this was a factory reset, which deletes all files & then you need to repeat the set-up and re-install your apps and files (Groan).
I then discovered the following Fix. Essentially, delete the Wi-Fi network details and manually re-input. A bit tedious, but much better than resetting to factory settings & reloading all your stuff! NOTE: It's NOT sufficient just to 'Forget' this network and reconnect to it.
1) Make a note of your Wi-Fi's SSID (network name). You'll also need to know the network security type (eg WEP, WPA, WPS etc), and password.
2) Touch Settings (the cog symbol) and the first entry is the Wi-Fi SSID the Tab thinks it's connected to.
3) Move the Tab 'out of range' of your router's Wi-Fi .. take it some distance away, or halt your Wi-Fi using a router command, or power down the router (first make sure you know how to restart it !). The Tab's 'Wi-Fi networks' must show your network 'out of range'.
4) Touch your Wi-Fi entry in 'Wi-Fi networks' to open a menu, then touch 'Forget'.
5) Find 'Add Wi-Fi Network' at the bottom of the Wi-Fi list, and touch to open a Wi-Fi set-up menu. Type in the SSID, select the security type, type in the password and touch 'Connect'.
6) Restart your Wi-Fi by reversing what you did in 3), and wait for the router to come up. The tablet should connect, so your Wi-Fi should now be at the top of the list and show 'Connected'. Touch your Wi-Fi entry, which should now show the IP address in use. If the connection still fails to start, you may need to repeat this procedure.
The problem should now be solved -- go on-line and check that your browser works!