It looks like advanced options are hiddent to non pro users, so here's the easiest work around. Since this is a home LAN, it should be acceptable security-wise.
Open up Zone Alarm and go to the Firewall tab that should be on the far left side of the screen. You should see two tabs in the upper right-hand corner of the screen. Click the one that says Zones.
In the lower right-hand corner, there is an add button. Click that, and then click Subnet in the list that pops up. This will bring up the Add Subnet window. Make sure that Zone is set to "trusted."
Beside IP Address specify your Network ID. (In your case 192.168.1.0)
For the subnet mask, 255.255.255.0, and call it something simple, such as "Local Network."
Click OK and then click Apply down in the lower right-hand corner of the window.
That does not expose your machine to the Internet, as IP addresses beginning with 192.168 are reserved worldwide as private IP addresses. Your machine is effectively hidden from incoming connections by your router's NAT firewall.
Hopefully that works. I'm not really that familiar with Zone Alarm, and this is just what I figured out after downloading and installing it.