Having a closed or limited NAT on your gaming console will cause a variety of issues.
The PS3 offers Type 3, Type 2 and Type 1 NAT results. These break down as follows:
Type 1 - Connected directly to the internet (no router/firewall). Should have no issues.
Type 2 - Connected through a router properly. Should have no issues.
Type 3 - Connected through a router without open ports or DMZ setup for PS3. Everything should function properly, but you may have connection, voice chat or other issues.
To obtain a NAT type 2 please ensure the following:
Your router is NOT double nat'd (connected to another router or modem/router). You can tell this by checking your D-Link's routers WAN IP address. If the IP address starts with a 192, 169, or 10 this usually means your modem is also acting as a router and is more than likely causing the problem. You would need to contact your Internet Service Provider/ modem provider to put the modem in bridge mode or to have them disable its routing features.
If your router is connected direct to a modem and is getting a proper public WAN IP address, you may need to open ports for the PlayStation 3. Typically TCP Ports: 80, 443, 5223 and UDP ports: 5223, 3478, 3479, 3658 need to be open.