Make sure that your new DELL laptop doesn't have a little switch to turn on the wireless that's built into it. If it does turning it on may be all that's needed.

You've not given much detail of your home network and the computers there, so it's difficult to know exactly what you've got there.

Is the PC a wired network connection that plugs in with a Network Cable (called CAT5 or Ethernet Cable) with fat phone plug type of connectors? If so that may be why the PC works ok.

I'm guessing that you already know wether you actually have WiFi Wireless in your network there. I'm curious if you configured it, or if someone configured it for you? If it's already set up and wireless is actually turned on on your new laptop, then you ought to be able to see the Network Name (called an SSID) in Windows Vista. Connecting to it should be fairly trivial. You usually have to supply a Network Key, depending on if, or what type of, security you have in your home WiFi Wireless Network. Something assigns IP Addresses and Network Router Gateway and DNS Servers to computers automatically. That something is called a DHCP Server. One of your networking gear should be providing that function. It should JUST WORK.

If it still doesn't, you need another Laptop or Wireless Client to confirm that your Wireless Network is in fact working. If it works with another computer, wirelessly, then chances are the problem is in your laptop.

* I do networking for mobile platforms mainly Marine/Motor Yachts. I have a web site: http://www.marinetelecom.net