Windows XP or Windows 2000, it's likely your loss of internet access was down to Microsoft's Windows Patch Tuesday update on 9 July, which ZoneAlarm really didn't get on with. (Vista users weren't affected.)
The quick solution: download and install ZoneAlarm's update - which ZoneAlarm released very quickly, kudos to them.
Specifically, it was a vital Microsoft security upgrade (KB951748) to patch vulnerabilities in the internet's Domain Name System which, in non-techie speak, could allow bad guys to fake things behind the scenes so that trying to go to a legit web address might actually take you to a different, malicious site which had "spoofed" that address, completely unbeknownst to you. (See this good explanation of the DNS security hole, and how Microsoft tried to close it but then ZoneAlarm blocked everything.)
Even the BBC reported the lost internet access problem yesterday, so widespread was it - so I probably don't need to as well... but it doesn't hurt, and it might help people who've not come across other reports.
(When I was first hit by this issue, I rolled back my PC to an earlier stage using GoBack, found out what the cause was, then uninstalled KB951748. When ZoneAlarm released their update, I upgraded, then installed KB951748. If you got rid of KB951748 too, make sure you reinstall it after updating ZoneAlarm as it's a critical security patch.)