You're entirely welcome John and Jeri. Deleting your cookies won't have any effect on the functionality of Zone Alarm.
One you've set your Internet Security setting to HIGH....go to the Shields Upwebsite have it "Test Your Shields" and "Probe Your Ports". The firewall should block it, but let it run its course of testing. In the end, what you should see is complete and total "STEALTH" mode on all your ports. This, is what you want.
I had no trouble using HearMe or ICQ, with the Firewall running.
Another thing to mention. If any of you have 2 computers (or more) networked to each other, and sharing a single internet connection through your primary computer (via cable or DSL, etc.) You will need to lower the Internet security setting to MEDIUM, in order for the other machines on the local network to access the Internet through the gateway your machine is providing. On MEDIUM, your computer will be visible on the Internet, but will still block any unwanted probes or intrusions. As I have 2 computers networked in my home office sharing a single cable modem connection, I keep the Local Network settings at LOW (to permit file and printer sharing between the two machines) and the Internet setting to HIGH, except when one of my kids wants to come down and go on the Net on the 2nd machine. Then I just drop the Internet setting down to MEDIUM. Once the kids are done, I put it back up to high.
Also, for those that have a permanent internet connection, and play games within Windows, you will want to prevent the Zone Alarm program from displaying notification prompts during gameplay, as these will lock up or crash your game. Rather than disabling Zone Alarm, the easiest thing to do, is before you start your game, go to the START button, and then RUN, and type in on the command line "winipcfg" (without the quotation marks), and see the network card used to access the Internet. It should be easy to spot because you'll see your IP address in the box. Just go to the bottom of the menu box and hit "RELEASE" and this will sever your internet connection. Once you finish your game, go back into WINIPCFG, and hit "RENEW" and that should give you back your internet connection. Any problems, just reboot.