Bypassing my firewall

Hey, /prog/.
I have a small home network that I dedicate to learning about computer/network security, because I plan to go into this field after I graduate from high-school.

I recently changed out firewall on my desktop pc because the old firewall didn't detect when I would connect to it remotely via my net-book, on the wireless network (not over the internet), using a simple rootkit. Now that the firewall is changed (it is now ZoneAlarm) it refuses to allow me to connect.

Which makes me wonder, are there ways to bypass the firewall and still connect, remotely (I'm damn sure there are many ways..)?
How could someone do this?
How could it be prevented?

I don't really want step by step instructions or hand-puts on how it could be done/prevented, I dislike that.
I'm mainly just looking for some hints on what to search for to find this out, and where to look and where to start.

Thanks in advance /prog/.

(The simple rootkit I had made is a netcat-like server, listening on a certain port, for a certain IP, onces that IP connect, it spawn a command prompt with system privileges, the client is then able to execute remote commands.
No worries though, I am doing this over my own network that is not online, and am using my own computers for this test, thus it is all being done legally.)

http://personalfirewall.comodo.com/Comodo_Firewall_2.3_vs_The_Leaktests.pdf

Run nmap (linux // redhat?) on a seperate machine...

Scan Everything

Go back to target and disable as many services as you can...(Preferably all the ones that showed up in the scan // that aren't being used/useful)

btw Nice job with netcat =)

Learn iptables.
Then learn cisco.
Then drop out of highschool and get a CISSP.