Sounds like you may need to open certain ports in the router's port forwarding and maybe add a setting in the router's DHCP Client List. Fortunately I was able to find an emulator on D-Link's site so i should be able to guide you step by step.
First, let's do the DHCP bit. Once you log into the router settings on the computer click the Advanced tab along the top and then click "Network Filter" in the menu along the left side of the screen. In the menu at the top select "turn mac filtering on and allow computers listed to access the network". Now, in the first blank type in the MAC Address of the PS3- you can find this by going to Settings/ System Settings/ System Information on the PS3. Once you have that typed in click the Save Settings button up above (you may want to do this for your computer as well).
Now, click on the Port Forwarding button on the left. You'll see a variety of blanks here- don't worry, we'll only need the top row. Before we start here, though, you may want to look up the IP address given to the PS3. You should find this over in the Status tab (look down to LAN Computers and find the one that matches the PS3's MAC Address).
Once you have this go to the Port Forwarding page and click the check box at the top of the list. Now, type "PlayStation Network" (minus the quotes of course) in the Name blank and type in the IP address of the PS3 in the IP Address blank.
You should be able to leave Application Name and Computer Name as they are- i did notice they have PlayStation 2 in the application list so you could try that if you like. Now, you have the TCP and UDP blanks. The ports that the PS3 needs open are these:
* TCP Ports: 80, 443, 5223, and 10070 - 10080
* UDP Ports: 3478, 3479, 3658, 10070, and 50100
Enter in the ports exactly like that, commas and all. Leave the last little menu showing Always and hit the Save Settings button. This should let your PS3 through to get updated as well as let you get going with the online gaming.