Does my router have a firewall or not?

Summary: Most routers both do, and do not, have a firewall. The good news is that the protection offered by a router's firewall is often exactly what you need.

I purchased and installed a broadband router. Specifically, a wireless Linksys WRT54G. I thought this provided a firewall and I had planned to uninstall Norton Systemworks which is giving me problems. However, the router does not appear to include a firewall. It does not need any sort of configuration like Norton, such as sites to let through or to block. I have looked all through the documentation and no mention of a firewall.
Did I buy a model without a firewall or was I mistaken about a router including a firewall?

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Your router does, and does not have a firewall.
And I totally understand that this is confusing.
I'll try to clear it up...

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One of the things that your router does is allow you to share your internet connection. By that I mean you can take a single internet connection that's designed to connect to only one computer, add a router, and then through the router connect several computers who can then use that single internet connection.
The way this happens is that your internet IP address, which is used to route data to you when you surf the internet, is assigned to the router instead of a computer. The router then assigns local IP addresses to each of the computers you have connected to it. The router then also takes care of making sure that the data sent to and from the internet is routed to and from the correct computer on the local network.

"... computers on the internet are completely blocked from connecting to computers behind a router."

One side effect of this approach, called Network Address Translation, or NAT for short, is simply this: no computer from outside your local network can initiate a connection to a computer on the inside of your local network.
Put another way: computers on the internet are completely blocked from connecting to computers behind a router. (You can create exceptions, of course, using something called "port forwarding" and/or "DMZ" settings in the router configuration.)
In this regard, the router is acting like an inbound firewall. In fact, it's acting so much like one that we simply refer to it as being a firewall.
Now, in the strictest sense, your router is not truly a firewall. Two key components are missing:

• Your router does not attempt to block any outgoing connections or data. A true firewall will typically examine outbound connections as well as incoming. In fact, a great deal of the configuration you referred to in your question is typically defining to a firewall exactly who on your computer is allowed to make an outboundconnection.
• Your router does not inspect the data that's routing, other than to make sure it's headed to the correct computer. Firewalls are often configurable to the extent that you can allow not just certain types of connections, but also allow, or block, certain types of data over those connections. In the extreme a firewall could actually incorporate anti-virus checking and block anything that was found to be carrying a virus.

So in that regard your router is not a true firewall.
So what do you need?
In my opinion: if you can trust all the computers on your local network, a NAT router provides 99.9999% of what you actually need in a firewall. Blocking external threats is by far the single most important role of a firewall these days; so much so that every one should have some kind of firewall, no matter what.
In my opinion a software firewall is simply not needed in this case. Blocking outgoing traffic sounds important, but in reality, if you have outgoing traffic that needs to be blocked, then either you need to change your system's configuration not to try to do whatever it's doing, or you are already infected with malware. In the later case, it's too late. The firewall did not prevent you from getting infected. At best it might have prevented you from infecting someone else, but even that is suspect.
Now, you'll notice I emphasized the phrase if you can trust all the computers on your local network. That's the one exception to the "software firewalls not needed" guideline. For example let's say you share your computer connection with your children who don't understand internet safety and are constantly getting their computer infected. In a case such as this, where you cannot trust some other machine that shares your local network with you, then you probably do need a firewall to protect you. And let's be clear; that firewall is not to protect you from the internet -- your router does that -- but from that other machine. And once again, what really matters here is blocking unwarranted incoming connections. As far as I'm concerned if the firewall lets you disable monitoring of outgoing connections, you can.
So if you're in that "safe" situation, then yes, in your shoes I would uninstall that software firewall and rely on the protection of my NAT router.
In fact, that's exactly what I do here at home.