"I run Norton and checked the firewall and all seems ok"
Thats part of your problem
The Norton firewall (besides being useless) is so difficult to make sense of that for many its impossible to know if its working. Taken alongside the fact that the antivirus part of the Norton programmes simply doesn't work very well, then I'd suggest the problem is almost self-inflicted.....
Run both of these two programmes over the machine and see what you find
Downloads - SurfRight
ComboFix Download