cannot connect to internet

We have an Acer Aspire 5750 and two days ago it logged itself off the internet when a security pop up told use a program was trying to access our computer. We did not recognise the program so blocked it and that is when it logged off. Since then when we try to connect to the internet it tells us to reset the router, which initially i did, but since the we have still been ok logging on to the internet through the same router but on our son's vaio laptop. So we assume it is not a problem with the router, but the Aspire. When I look at the network center it shows an unidentified public network between the aspire and the internet which appears to be the cause. I have tried a system restore but this hasn't helped. Could someone give me an idea of what the problem is and any way I could fix it please?

The "unidentified public network" could be any router within range of your computer that you are not logged into.
The sudden disconnection from the 'net is a bit weird and could possibly be a viral attack that may have got through, or your internet security decided the threat was so great that it logged you out.
Have you tried looking in the network connections and deleting any existing wi-fi set-up, then do a new search for your router and set it up anew with your router's network key?