I have Zone Alarm installed on one of my systems. I no longer use it, but it is not uninstalled, I just don't start it up much anymore.
I installed XAMPP on two other systems, and it worked just fine. One is Windows 98, the other Windows XP Professional.
When I installed on my third system, Windows XP Professional (the only one with Zone Alarm), it would not work. Everything showed as "Deactivated" although Apache and PHP seemed to be fine. MySQL was definitely unreachable. It could be started, but not stopped, etc... Lots of strange things. PHPMyAdmin could not find MySQL, nor could any of the examples.
To fix this:
Make sure XAMPP is not running. (check Windows Task Manager if you are not sure, you may need to shut down mysqld, etc)
Start Zone Alarm
Grant Permission as needed
After that, you can shut down Zone Alarm and don't need to restart it each time.
The problem is that if Zone Alarm is installed but not running it will still block the new installation of MySQL, and probably other things, too. The solution is to START ZONE ALARM if it is installed but not running.