unknown connection??

[Jayme3]

Hopefully someone has some ideas to help us.  Since Tuesday our computer has said that there is no internet connection although our modem says that there is a connection. When you put the mouse over the 2 little internet screens it says that it is an unknown LAN.  We have double checked the IP addresses, restarted the computer/modem a thousand times.  Yesterday Verizon tech said that it was a problem on their end (something w/ central processing) and said service would be up by 1am.  Surprise, surprise it wasn't.  At 10am -we were called the issue was fixed.  Restarted the computer/modem and again the modem says we have a connection but computer says we don't.  Another 2hrs spent on the phone w/ Verizon only to be told it's our computer.  Any suggestions/ideas?    Everything worked fine until  Verizon had their "central processing" problem.  

[walt178]

In the network settings on your computer, is it set to obtain IP address and DNS server address automatically?