Vista - While I am already using the internet I get Limited Connectivity

I have Windows Vista Home Premium 32Bit on my gateway laptop. I was getting this same problem with Cox internet so I switched to Verizon Fios and I am still getting this problem. It randomly happens and varies. I'm using the internet fine then out of nowhere the connection says I have "Limited Connectivity". Sometimes this happens 5 minutes in or sometimes hours. When that happens I try to disconnect from the connection and the box just freezes and I cant open Network and Sharing Center either. Diagnosing doesnt help either. So I am forced to restart my computer. Even when I do that it restarts REALLLY slowly. Then when it finally does and I sign back in, it says Windows had an error or something like that and it can find the solution. This problem is making me . Sometimes when Im looking stuff or watching a video the internet just stops working and I lose the information.
Anyone know the problem??

Someone help please. It also says I have a problem with Domain Name Server?