How will you know that your LAN card is damage

You know the LAN card is damaged when a second card works with no issues. You say you can't open one of you browsers, are you saying another browser works? And by open do you mean it does not go online or you can't even start it?

Start a command prompt and do an "ipconfig /all" command, post what it shows you for IP/DNS/Gateway.

Ping 127.0.0.1 if that doesn't succeed you either have a bad NIC or something screwed with your TCP/IP protocol stack. Also do what hang-the-9 said. You can ping your gateway IP and post that info if you get a chance. That will let you know if you can communicate with your router.