I just switched from a Windows laptop to a MacBook. On
my old laptop I used a wireless card to connect to the
internet (I have a linksys router) and had no problems at
all. On the mac is AirPort, and linksys comes up on the list
of networks to connect to. I select linksys and open Safari,
but it always says I'm not connected to the internet, even
though I have full bars on the AirPort sign. Then, it says I
should try Network Diagnostics to rearange some
settings, but I have all green signs and I get the message
telling me my internet connection seems to be working.
I've tried shutting off and restarting the router, I've been
on the phone with technical support for hours playing
around with the network diagnostics, but nothing works!
Can somebody get my internet to work with my router??

(I'm only on the internet now because I'm connected to my
neighbor's network...)

Need more details to assist w/ this one.

Are you assigned an IP address?? Open a terminal window & run 'ifconfig' - see if you have an IP assigned to your NIC when it says it's up.

Try to traceroute something & see how far it gets -- i.e., traceroute -d google.com

Also, is the firewall off?? I think it's somewhere under System Prefs / Services -- make sure it's disabled.

Open Network preferences in System preferences. Double
click on Airport. The click on the heading TCP/IP. The
second thing in the list should be IP address. Is it
192.168.1.x? If not, the the Linksys is not handing out an
IP address to your Mac.

Do you have MAC address filtering or any other security
features turned on on the router?

Anotherthing to check is the router DHCP client list. Using
a web browser, go to the router utility/set-up page. Under
the DHCP heading, click on DHCP client list, is your Mac
listed there?