Have an older (Version A series) D-Link Dir 655 that gave me fits when I tried to use Wifi on my new S4. The problems were: (1) If I was on my computer when I activated Wifi on the phone, my computer lost Wifi connectivity and the phone, while connected, could not access anything; (2) while the phone was on Wifi, it's data functions were basically bricked--no Wifi and no 3g. D-Link just put a firmware update on their website to address this issue, which can be downloaded at http://www.dlink.com/us/en/support/product/dir-655-wireless-n-gigabit-router?revision=us_reva. This solved the problem for me. The firmware fix resets the router completely, so be sure to save your configuration before installing. Ting Help didn't have a clue about this problem, so hopefully this will provide some help for any having the same trouble.
Galaxy S4 incompatibility with D-Link DIR 655 Router Fix