You are right about considering another firewall, but let's give ZA one more chance!
Let's clear the slate!
First, enable the SP2 firewall.
Second, using the ZA Pro uninstaller, uninstall ZA. Restart your computer. For that go to Start All Programs and head to the ZA icon, there I think you will see the ZA uninstall option. If not just use the remove option in Add/Remove programs.
Now,update your antivirus software and run a full system scan. If you have Ad-Aware and SpyBot, update each of them and run them. Restart your computer.
You may have to repeat one some or none of these next steps.
Now go to Start, Search, All files and folders, go to More advanced options ,click each one except "case sensitive". Now type Zone Alarm into the search bar. Delete every entry you can. Restart your computer.
Now, follow the same steps except this time type in Zone Labs. Delete every entry you can. Restart your computer.
Before you complete the next step which requires working in the registry, make sure to back up your registry. Backing up your registry is just good sense anyway.
Use these links to help you with that process. It won't take long and it is sound insurance.
Now let's go into the registry and get rid of ZA there. Be careful here. Follow my instructions precisely. First, go to Start, Run, type regedit click OK.
All Right we're here. Now go to Edit at the top of the window. Click Find, type Zone Alarm, Click Find. Delete the entry.After it finds the first entry click Find Next. Delete every entry you can provided it says Zone Alarm. Restart your computer.
Now repeat these steps but this time type Zone Labs and delete every entry you can. Restart your computer.
Now reinstall ZA and make sure permission is fully granted to Mozilla and IE. In fact grant permission to every program.
Now see if you can get out on the net. If not, disable ZA, then go out on to the net and reenable ZA. This is an attempt to train ZA to accept IE and Mozilla access on and to the net.
Just to be safe , let's get a second opinion as to the integrity of your system. Let's go to House Call for a free virus scan at : http://housecall.trendmicro.com/housecall/start_corp.asp
Now if you are clean and still have the same problem, then it's time to consider a new firewall.
If the free ZA was working maybe go back to that. It is not the total security package that ZA Pro is but it is still a good firewall. However, there are others that offer great security features and will work on your system.
I recommend OutPost http://www.agnitum.com/products/outpost/ They offer a free and a pay version of their firewall. Be careful with Outpost if you are using McAfee virusScan 8. and Outlook. There is a serious incompatibility problem there.
There is also Norton 2004. Get a three month trial of it here : http://www.microsoft.com/windowsxp/downloads/updates/sp2/antivirus/default.mspx.
In fact, I recommend every product on that Microsoft page. If I were you I would try Trend Micro.Their firewall is not permission based,rather it inspects (filters)every program (packet)that accesses the internet. You don't even know it's there unless it catches something. However, if you are using an antivirus, you will have to uninstall it if you want to go with Trend Micro as Trend Micro is a firewall and antivirus package.
If the firewall you try does not work out, then make sure you go through the removal process I described to you above.
Keep me posted!