You don't have to shut down Zonealarm to get the two to talk. It just needs to be set up correctly.
Here is the step for it...
Step 17(optional if you have a network in your house) - If you have a network in your house and you share files and/or printers, you will need to configure a Trusted Zone for the rest of the computers in your house. If you do not do this you will not be able to share files or printers. To configure a Trusted Zone, select Firewall on the left side of the ZoneAlarm control panel. Next click on Zones on the top right. The screen will then show the zones set up on your computer.
Depending on how your network is set up, the IP range that your network runs may differ. If you have a LinkSys router your IP range will probably have an IP range of 192.168.1.100 to 192.168.1.150 and you can set up your Trusted Zone like below. To get the screen select Add -> IP Range. After you enter in the information click "Ok". After that click "Apply".
ZoneAlarm trusted zone.
If you have a different router, the IP range may be different. If you don't know the IP range of your network, you can add each computer in your network to your Trusted Zone. This is done by finding the IP address of each computer in your network and adding it to the trusted zone by selecting Add -> IP Address. You will also want to add any network printers you have.
edits : I copied the Zonealarm from a helppage I have...didn't realize how long it was.