When I sign in with my hotmail account, I get this error:

Live Mail does not recognize my internet connection. 

Then if I try my Verizon account I get this error but I think it's for the same reason.  Unable to send or receive messages for the Verizon xxx account. The host 'pop.verizon.net' could not be found. Please verify that you have entered the server name correctly.

Windows Live Mail error: 0x800CCC0D

Socket error: 11004

My internet connection is working but Live Mail does not recognize it.