I'm sitting behind a restrictive firewall for both outgoing and incoming traffic. I'm trying to find some way for me to test which ports are open and which are closed. For example, if I try to connect to a service and its refused I need to find out if the problem is that the port is blocked on the firewall or if the service I'm trying to connect to isn't functioning correctly.

Thanks for the help!

How about to see which services are running/listening?

And you could try an nmap scan from another machine on the same network to see what the firewall has closed.

You could use a good port scanner ( I suggest "nmap". "nessus" is good too but harder to configure) to scan your computer from inside and from outside.
The idea would be to acan from an external source that you know to not be firewalled... this would give you an idea of "what" is accessible from the outside.
Then from the "inside" network, you could scan your external box, making sure "ALL" ports are opened and listenning on that box (an easy iptables script could redirect all port to a single one, showing them all open). So you would get an idea what is able to "get out".