Need Firewall When 'Puter is Off?

I've been using Zone Alarm which activates upon boot up while I've had a dialup account for years and felt very safe. Now I've switched to DSL (finally!!) and am wondering if someone could harm my computer when it's off and Zone Alarm is not active? I have a laptop which is prone to overheating, so I have to turn it off. Do I need protection when it's off, and if so, what? Thanks!

 

Along those same lines.... we also finally upgraded to DSL. My understanding is, that even if the browser has not been activated, we're still "connected" so to speak. We have a router/modem as well as individual software firewalls (my wife and I are networked). So, I'm wondering.... if I go upstairs for half an hour, do I need to disconnect from the internet to be "safe" from hacking since there will be no browser activity OR would that not afford me any more security since even with the browser disconnected, I would still be "connected" by virtue of the DSL and my computer being "on "?

 

As long as you have the software firewall enabled, you're 99% safe.

Software firewalls will block incoming as well as outgoing packets as needed.

Edit:
Wanted to add as long as you are careful on what programs you grant permission.

 

As Tony stated, off = safe.

BUT ... with most modern PCs, off <> off (not equal) but will be some sort of deep-sleep resting state even though it looks to be off.

Depending on your hardware and settings, it is possible for a remote signal to cause the PC to boot up. There is a feature within the BIOS of many PCs to allow a signal to the network card to turn on a machine that is off.

 

With my desktop PC, I can physically disconnect the external modem. If I had a problem keeping ZA on (which I do not), I think I would be safe when I turned ZA off if I disconnected the modem. But I do not know if/how you can disconnect the modem with a laptop.

 

So, is Zone Alarm enabled when the computer is off? I was thinking it wasn't loaded (is that the same as enabled?) until I boot the computer.

 

Well, my laptop's not really modern -- about 4 years old, so I have that working in my favor.

I have an external modem, so it's easy to just unplug the USB cord as Welshjim suggested.