Wireless Internet Isn't Working

I have a laptop that has a wireless internet function, but it won't work (hence the title). I have a router connected with my cable internet, and I can locate the signal with my laptop. I can get it to connect except it gets "limited to no connectivity" (meaning I can't get online). It says the cause is that the network didn't assign a network address to the laptop. If I try to repair it, it will try to renew the IP address but won't be able to.

A similar thing happened to my friend's laptop a couple of weeks ago. We were at the mall, where there is wireless internet, and he tried to connect with his laptop and got about the same treatment as I do. I do believe he gets internet on it at home, but it may not be wireless, I don't know.

Can anyone shed any light on this?

Another bit on info: The connectivity doctor thing on the laptop says that the problem is that the IP address was not set properly.

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Please tell me this is a joke, no one can be this stupid.

--For windows XP--

 Go to Control Panel --> Network Connections --> Right Click on the Wireless connection and go to "Properties". You should see a box with the words "This connection uses the following items". Select Internet Protocol(TCP/IP) and press the properties button. There should be two buttons you can select; "Obtain an IP address automatically" or "Use the following IP address. Select the "Obtain IP address automatically" button and click "ok". You just enabled your DHCP client. DHCP is a protocol  that "grabs" an IP address for you. Do the same thing on your friends laptop to get internet access at the mall.

More info...
http://en.wikipedia.org/wiki/Dynamic_Host_Configuration_Protocol

Thanks >>4 but the DHCP was already enabled. I've gone through it again doing what you said, but it turns out the same.

I was connected to the network (without actually being connected) and restarted my laptop without disconnecting, and when the laptop restarted, it said that I had a good connection, the way it should be. However, I tried to visit a site and couldn't get again. I hit "repair" in the connection properties, and it went to the same old thing - couldn't renew IP address.

The connectivity doctor on the laptop says that one cause of it may be that MAC address filtering of the Access Point may not be set properly. I've never checked this out because I don't know how to. Can anyone help me there?

Read the fucking manual. If your wireless router belongs to you as you claim, you would have received a manual with it. It will tell you the correct operation procedures.