I need to make a more detailed webpage on this stuff some time.
Your IP: It's needed, you can't make requests for thing without it, otherwise how does the server you are sending the request to know how to return the data to you? You send a letter to a company for a job, if you dont put your address in it, how can they reply?
Blocking IP is therefore not possible unless you go do your tasks through a remote server, such as a proxy server. You send your request through a proxy, so that the server actually sees the IP of the proxy server. It then knows to return the data back to you, and as long as its stated as an anonymous proxy, it wont insert your IP address in any way.
Johnson is right, people randomly send data/pings to random IP addresses. A good firewall will not respond to such data, making the potential hacker thinking you are not there, some basic firewalls just stop access, they respond to the packet making it clear you are there.
You said he used your IP address to access your PC. If this is true, then you have a trojan horse installed, which is allowing him to remotely control your PC. You need to then scan your PC to find and remove this Trojan Horse, if you do have one,
http://www.simplysup.com is free for 30 days. You can uninstall after 30 days without payment. If it's clean, chances are he never accessed your pc.
Dial Up users get a new IP each time they reconnect. Cable and DSL users is not always so, but you can usually ask your ISP to assign you a new one. My ISP gives DSL users a new IP every logoff, or every 72 hours. If you are using DSL, you should look into using a good firewall, not necessary one you need to pay for.