You can use the Ethernet cable to connect the computer to the router.If that works then it is a wireless problem and there is more possibility that I it is a wireless security.Verizon is dedicated to protecting consumers and businesses from identity theft.
My wife was also having the same issue with her laptop and she did the same and now she is not getting the issue.
You should also do that and I hope this will help you too.
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I just installed a new Linksys ADSL modem/router at home.
Edit: since you have just reformatted the xp machine.
ensure that the wireless drivers are updated to the latest version.
Select the wireless network tab and click on properties and open the "Authentication" tab.
There you have to uncheck the top box "Enable IEEE 802.1x authentication for this network".
First of all go to the "Wireless Networks" tab and then open the properties of the wireless network to which you are trying to connect.