If the printer has an IP address assigned, be sure that IP is included in the Trusted Zone in ZoneAlarm. If it is connected to another machine, be sure that machine's IP is also added to the Trusted Zone. 

First step

• Open The ZoneAlarm.
• Select Antivirus & Firewall
• In the Advanced Firewall section click on Settings
• Make sure Your Trusted Zone is set to Medium security
• To add the IP address of your printer click the View Zones button
• Click the Add button and select from the menu IP Address
• Enter your printers IP address in the space provided and add a description then click the OK button
• Close ZA and restart your PC and try to print.

You should download the very latest drivers for your model from the printer manufacturer's web site. Remove the old driver, reboot, and the reinstall the new driver with ZoneAlarm Products running (force it to overwrite files if asked). 

If that does not solve your problem, contact ZoneAlarm support.