|Most routers come with a built in firewall and any half decent firewall will reject any unsolicited requests to port 80, unless of course you are hosting a web server. It is called state full packet inspection. Most SOHO routers have it as standard.|
A hackers cant do anything unless you have some malware on your computer that will respond to an incoming request.
A decent firewall can be configured to reject ICMP requests which is used by the ping command. Once ping requests are blocked your computer is to all intents and purposed is invisible on the Internet.
Try pinging 126.96.36.199 which is my IP address. You wont get a response even though port 80 may well be open. That is called stealth mode in most firewalls.
Check here to see how well configured your firewall is.