Hi Roxanne,
I'll take a shot at it based on what I'd do and what I would do if I were more concerned about vulnerability;
You have a router (Missed my guess on the brand

)so I'd test to ensure your firewall type features of blocking unsolicited inbound requests are active. You can also turn off answering PINGs if you wish.
Then install any available updates to your security applications and perform any scans they provide.
Using msconfig, uncheck weatherbug(weather on my system) from startup if you want to keep it. I don't find anything objectionable to me in Wxbug but I regularly scan my PC for adware and other crapware too - just in case.
After you've finished your housekeeping, test with something like grc.com, BBR tools or other popular scanner to see if your router and ZA are doing their jobs.
As I said before, there's reasonable evidence to believe the ZA window could present a vulnerability opportunity, but as of today no exploits are known and I feel exposure small for anyone with typically implemented security apps and configurations.
Based on what I've been able to discover Zone Alarm has been silent, even to its Team Z members, on the issue of the potential vulnerability.
If, after your own research, you feel uncomfortable with ZA's protection during the window, you might disconnect by using the disconnect feature on newer RoadRunnere modems, power off the modem or unplug the ethernet cable until your PC has powered up completely.
Switching to another ZA-type product may not exempt you from this relatively small "hole" as I am seeing reports in this forum of other products behaving similarly.
I hope I've provided you with acceptable solutions while avoiding any initiation of flame wars in this topic between folks who differ on ZA's potential exposure.
Have a great day,
EG
Edit - Corrected lousy spelling, syntax and capitalization
