Can't connect to Internet

Hello,
Not sure about the forum--novice computer user. I have windows vista on my laptop (wireless--DSL). Problem--I cannot connect to the internet. I called Verizon and asked for help. I was told my NIC card was bad. What confuses me is that the computer says I'm connected. I can't get online with my line but I can connect through an unsecured site. If the NIC card was bad, why can I connect using another line? Please is there anybody out there that can confirm Verizon's diagnosis or help me with this problem? I'd appreciate any help.