By checking your firewall's log you should be able to find out exactly what was blocked, as well as what IP address it came from. Then, to obtain more information, check out CheckDomain. Just type in the IP address into the online database and it will tell you who registered the domain, as well as their contact info (address, phone number, e-mail, etc), if available.

However, if the person is using, say, Time Warner Cable, it will give you Time Warner Cable's information, not the end user (their customer). That's by design, so there's little you can do about it. However, if the person is trying to hack your computer, you can print out your firewall's log and call the ISP (in this example, Time Warner Cable) and tell them what's going on. They can check their records to find out who was using that IP address at that time, then take the proper action.

Note: A person's IP address can change quite often. Those who use dial-up will usually receive a new IP address each time they connect, while someone on cable/DSL can usually receive a new one by unplugging their modem for a few minutes. Thus, the exact time of the intrusion is important...the ISP will have to check their records for the IP address at that particular time.

Hope this helps,
John