Buying a Router with built in Network Address Translation [NAT] can stop any ports from being a threat from the WAN [Internet]. Packets get to your Router that is also a firewall and filters out unwanted / unfriendly packets. A cheap Router like SMC 4 port 10/100 switching Router goes for $40 and upwards [USD].
Over simplifying it.. NAT works like this... you have an internal lan-locked ip address [eg], your Router has a world viewable IP address assigned by your ISP. All packets you send to the 'rest of the world' get handed to the router which in turn rubber stamps them with it's ip address but keeps the senders information in a special table. When the packet is responded to [say a response from a webserver after a webpage request] the router will pass back to your ip address the responding packets.
If a cold calling packet, one that is not initiated by you, your network or your router, and one that is not allowed by the router, happens to come to the router [a ping or port scan for example] the Router can automatically ignore it depending on the make, model of the router and the setup. Routers out there can also double up as gateway antivirus scanners, mail agents, webservers and more.

This is an outside the box approach to protecting your ports that requires little or no tech-knowledge and a quick n cheap fix to such a problem. It's also the first step to a centralised way of safekeeping a home network.

Ciao for now... Kwi