depends on how your router and laptops are set up.
we are going to get onto your router's web based interface.
try a wired connection to one of the ports on the router.
because the option of only allowing wired devices to configure settings on the router MIGHT be turned on.
now, like said by others, try 192.168.0.1, 192.168.1.1, or 192.168.2.1 (these are the most common) in your web browser (Internet explorer, Mozilla firefox, Google chrome). Sometimes it is different than these addresses (this is the address of your router that you are typing in, or "default gateway" because your router acts like a gate, that's how I like to think of it), again, depends on your router, and how it is set up. you can see what your default gateway is if you cannot get to your router's web-based interface. go to network connections, click your connection that you use to connect to the internet, right click, go to my properties, click on the TCP/IP protocol, click properties, then you might be able to see it there, if not right click on your network connection in the lower right of your screen (in the quick launch bar, with the start menu bar) and then click "status" it might be there, (what you are looking for is the default gateway by the way). if not, go to your start menu, click Run (I am using XP, vista and windows 7 I do not know how to do this, but find the "run" program in your operating system. type "cmd" in the "open" field, then hit enter. once there, it should be a black old school screen waiting for you to type something. Type "ipconfig" and It should be there.
once you have found the default gateway, type that into your web browser. now there will be a screen that asks you for a username and password, usually it is admin (username) and blank (for the password) if this does not work, try administrator for username and admin for password, all routers are different, fiddle around with all of those and try different combinations of username/password. user-name/password should also be on the back of your router as well. Or in the case where someone has hacked your router and set up their own username/password, then reset the router, which can be a pain to get it back up and running if you do not know your modem's password, in which case you would have to call bell or rogers or whoever your ISP is.
once you get into your router's web-based interface, it could be a bunch of problems, could be that MAC address filtering is turned on, if so, turn it off, or allow your new laptop in the "allow" list, It could be that DHCP is not turned on on your router, if so turn it on, or you could manually assign your laptop an ip address and DNS server(s), but that is a longer process. It could be that you have a password or keyphrase on your router that you do not remember you have on it, and you cannot remember the keyphrase or password, in which case you would have to reset your router. (and get your modem's password for connecting to it, to connect to the internet, which is what you probably want).
could be that your new laptop only accepts WPA and WPA2 password/keyphrase encryption, while your old laptop only accepts WEP encryption and not WPA/WPA2, in which case you would either have to get two routers, one for each laptop and have one of them WPA/WPA2 encrypted, and the other WEP encrypted, or just turn off Wireless security/keyphrase/password on the router, but you probably want some kind of security on the router, so if this is the case, use mac address philtering and turn off wireless security, unless you want to get two routers for your network.
your new laptop may not have a wireless card installed on it, in which case you would have to purchase a USB wireless adapter probably. but this is probably not the case if you can search for wireless networks and they show up, and you say that you can connect.
Is there a yellow triangle with an "!" in the middle of it infront of your internet connection symbol in the quick launch bar located on the right of your start menu bar?
if so, then DHCP is turned off on the router, or MAC Address filtering is turned on, or you have not entered the keyphrase correctly or at all yet.
in which the solutions are typed above.
there ya go! post again if you have any trouble.