From what I can tell after a quick search... Zonelab(s) used to be the company that did zone alarm, which is now owned by checkpoint... (yeah... go corporate america!)
They redirect right to the zone alarm site... I currently run the Firewall/anti-virus combo, so I am not sure if this will work for you...
Right click on the "Z" icon, lower right corner... there is a list, enable internet lock, stop all internet activity and game mode. I lock out the internet completely, then enable game mode with all set to deny.
According to the website, these are not available in the free version. The only way you could do it then is to suspend the program, or go into the options and then set alerts to off. I have always had alerts set to off, even back in the days of using the free zone alarm. It just shuts off the pop ups, which is what is causing your troubles. Those are found by clicking the tabs on the left side of the actual program. Right click the "Z", and restore the control panel...
Hopefully helpful... And not to be a salesman, but the $30 I spent on the AV and FW together has been well worth it. I'm going on the third year now... which only cost me $19.99... No hassles, no worries, no update issues. Alot nicer than the freebies I lived off of for so long.
T