Jimmy where are you coming up with zonealarm and pirated software from, it could just as easily be nortons internet security suite (ack pooh). And as he by his own admission is not computer savy he isn't so likely to be using pirated software.
MACS, if they are being blocked by your firewall you don't have much to worry about. I personally don't like norton, but if its working for you then thats all that really matters. It could well be someone scanning a block of i.p. addresses looking for weak spots. If your firewall is any good it will have just dropped the request and the guy on the other end won't even know there is a computer hooked up to your IP.
If you find yourself in need of help drop me a line with some details
fudge !at! watchtv !dot! net