Actually, most recent wireless routers can do DHCP. This would make setup much easier than using fixed IPs as it would set the DNS, gateway, default route, etc. for you automatically.
How is it configured in Windows? Are you using DHCP there? If not, you can use the same settings you are using in Windows. If you are using XP, you can open a command window (Start, Run, cmd.exe) and type 'ipconfig /all <CR>' to get a listing of the network settings. You may want to print this to use as a reference for Linux. (By the way, '<CR>' means to hit the return key)
I've not used Ubuntu but I suspect it's similar to other flavors of Linux. In the networking setup you should have a place to specify the IP address, the subnet mask (very important!), and the DNS IP address. There may also be a place for you to put in the default gateway, which adapter to use, and route information.
If the laptop has more than 1 NIC (sounds like this is the case), if your wireless is on the second one, you may have some problems. If this will only be used on wireless, you will probably want to disable the other NIC, or actually remove it from the network configuration. If you don't, Linux often won't set up the routes for the second NIC even if you do use DHCP.
A bit of debugging you may want to do: If it looks like the box is connected, see if you can ping the router by its IP address. For instance, many routers default to 192.168.0.1 or .2, so you would open a console window and type 'ping 192.168.0.1 -c 5 <CR>' (substitute the IP of your router if needed). The '-c 5' says to only ping it 5 times instead of continuously. (This may vary with different distributions.) If you can ping it successfully, that's half the battle. Here's what a successful ping looks like:
$ ping 192.168.0.1 -c 5
PING 192.168.0.1 (192.168.0.1) 56(84) bytes of data.
64 bytes from 192.168.0.1: icmp_seq=1 ttl=64 time=73.1 ms
64 bytes from 192.168.0.1: icmp_seq=2 ttl=64 time=4.23 ms
64 bytes from 192.168.0.1: icmp_seq=3 ttl=64 time=4.04 ms
64 bytes from 192.168.0.1: icmp_seq=4 ttl=64 time=4.20 ms
64 bytes from 192.168.0.1: icmp_seq=5 ttl=64 time=4.08 ms
--- 192.168.0.1 ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 4015ms
rtt min/avg/max/mdev = 4.042/17.945/73.157/27.606 ms
$
If this works, that means you have the IP and subnet mask correct, and the proper NIC and default gateway are right. If not, you need to check these and get them right.
If you can ping the router, then you can try 'ping
www.google.com -c 5 <CR>'. If it says it can't find the address, then you likely have an incorrect or missing DNS entry. If your Windows configuration shows 192.168.0.1 as your DNS server, then if you 'cat /etc/resolv.conf <CR>', you should see a line that says "nameserver 192.168.0.1", and possibly other lines. If it is empty, then you will be unable to convert hostnames to IP addresses, making life rather difficult. You should be able to put in the DNS address in your Network or DNS configuration, depending how your distribution handles it, or you could actually edit the file directly, though some distributions may detect changes to certain files and change them back if they weren't modified with the proper program. Check out this much and see where you are.
