If you're not even seeing the name of the router when you search for it, it's likely that you don't have SSID broadcast (radio) enabled on the router. Make sure it's enabled and let me know if you still need help.
If you configured everything else connected to your router, then you probably know how the DS should be configured and the SSID isn't the problem. I'm taking it in little steps for now.
Also see if this helps at all:
| Nintendo - Customer Service | Nintendo Wi-Fi Connection
Don't let PSP owners use that as a reason PSP is better, tell them to try connecting to your router before claiming it's the fault of the DS.