I was wondering, does a firewall continue to guard your computer when you log off, but don't turn off the computer?

I use ZoneAlarm on Win98.

As long as the resident firewall in enabled, it is running, and whether you are connected to the NET or not doesn't matter. However, its benefits when you are NOT connected are extremely limited.
Regards,
John

So, if I log out of Windows, my firewall is still running, but my computer isn't completely protected?

Yes, but remember that your firewall only protects you from online threats. If you're online, your chances of getting viruses, spyware, hijacked etc are much greater. However, if you have a firewall enabled it should keep out those nasties. A good firewall to have is the one from Zonelabs, (Zonealarm). I find the built-in firewall in windows XP not bad though, it is the one I use.

When you are not online, or doing "on-line activities" like reading previously downloaded Email, your computer is relatively safe; it is not that you are not completely protected, it is rather that you don't need the same high level of protection (hence you scan your hard drive with your Anti-virus).
To conserve CPU usage, I generally exit my resident firewall when I am not online and doing activities requiring a lot of processing, and do so with perfect safety.
Regards,
John

Really? Looks like ZoneAlarm is blocking almost as much stuff while I'm logged into Windows, but not using Internet Explorer.

Oh, okay. But what if I'm not logged into Windows at all? Does the firewall block anything then? I know the threat is substantially reduced when I'm not on the Internet, but it looks like ZoneAlarm starts blocking threats as soon as I log in to Windows. I used to keep my computer at the Windows login screen when I wasn't using the computer, but I was thinking maybe the firewall wasn't blocking threats, so I started turning off my computer whenever it wasn't in use. Since I use my computer a lot, it can be a hassle.

It may be simply Z/A informing you of application changes made when you updated them, or giving you notice of internal communications between applications. Without seeing what the messages are, I cannot say for certain that it was or was not blocking "threats" or simply doing something else.
If Z/A launches on boot up, anytime you start Windows, it should be running whether or not you are on the Net.
It is a good idea, if you are not going to use your computer for a protracted period of time, to turn it off; this not only saves electricity, but allows it to reset itself (whenever you see the Windows screen, you can assume that some part of the Windows OS is already running or you would not see the screen itself.
Regards,
John