Does it say Request timed out or Destination host not found

Mine is set up with a belkin ADSL modem with wireless g router - IP settings as follows

Go to network connections - right click local area network - find Internet Protocol TCP/IP on the list - click properties - add your ip address as required

I guess it will be;
IP Address - 192.168.2.(2-9)
Subnet - 255.255.255.0
Default gateway - 192.168.2.1
DNS - 192.168.2.1

Apply OK

Might work for you

What WiFi "router" do you have? Please give brand/model/make.

Who is your Internet Service Provider?

What WiFi card do you use on your computer?

What operating system are you running on your computer?

(This sounds like your "router" is only a bridge, or is in a bridging mode.)

Is this connection encrypted? If so, do you have the Network key? Even if its encrypted, sometimes it shows that you are connected but it won't let you send/receive packets, I've noticed this when you go to View Available Wireless Networks, it will show you all the ones in range and whether they are encrypted or not.. so just for fun one time I tried connecting to a neighbors connection, and it said it Connected, but no packets were coming in or going out because it was encrypted, not open.

The only way he can get a public IP is by having that AP set up as a bridge and most likely without WEP. (Are you sure it is a public IP? What are the first two octets?)

I am still not clear of your setup. You have WiFi into your house? Or some sort of a line (cable/DSL/Modem/Leased line/etc.) and then off of that you have a WiFi link?

Or...are you trying to connect to your neighbors wifi signal?