Some part of Zone Alarm is remaining on the system there. The first thing you need to do is disable all ZA items shown in both the startup and services sections in the msconfig utility. The system configuration tool was included in Windows for this type of problem since 98. Simply type msconfig at the Run prompt off of the Start menu, click the ok button or press the enter key in order to see the new screen appear.
The last tab on the right hand side os for the items that automatically load along with Windows at boot time. You simply click the startup tab and uncheck any items for ZA there. From there the services group is next door where putting a check on the "hide all microsoft services" box removes worry about disabling an essential system function.
Once all items are found and disabled you click on the apply button before exiting where you will see a prompt to restart the system. Upon the reboot all ZA items will be totally inactive ready for removal. See if this method takes ZA off without trashing your connection.
