For the most part, this has very little to do with the Bios on your machine.
The two programs that you reference perform different functions. This could probably be explained in more detail, but basically:
- The Antivirus protects your machine from viruses coming in.
- The Firewall protects you from people coming in and data getting out.
The ZoneAlarm is a Firewall software and Symantec's Antivirus program is Antivirus. If the version of Symantec's Antivirus that you are using contains Norton Personal Firewall, than you to not need ZoneAlarm, because Norton is providing the Firewall.
If the ZoneAlarm Firewall is the only Firewall you have installed (the Windows Firewall does not count), than you should probably leave ZoneAlarm installed.