The keys to successfully uninstalling Zone Alarm is to make sure it is not running while uninstalling and plenty of reboots. What I mean is this:
First, with ZA running, opening its user interface (Control Center) by right-clicking on the ZA icon in the systray and restoring its control center. Select the "Overview" panel > "Preferences" tab > and uncheck the "Load ZoneAlarm Pro at startup" option. There should be a popup asking to confirm this action which you need to allow. This will ensure that at the next reboot ZA is not started.
Then reboot the PC (this is important!). Verify that ZA has not started and even check in Task Manager (ctrl alt del) to ensure none of these is present: zonealarm, zapro, zaclient or vsmon.
Now simply use the Add/Remove Programs uninstall option to deinstall ZA. If you've prevented it from starting and rebooted first, then you should get a clean uninstall.
Reboot after the uninstall, if it didn't force you to reboot on its own, and check for files. There should not be any, but just in case look in: \Program Files\Zone Labs\ and under Windows\Internet Logs\ and Windows\System32\ZoneLabs\
Almost all problems uninstalling Zone Alarm are related to it either being running or having its files locked because they were running during the current booted session, which is why I advise the preventing of loading at startup and a reboot prior to even trying to uninstall it.