Some routers aren't configured to pass ICMP - and many firewalls are configured to block as well. In addition, some ISP's block ICMP echo requests, replies and/or TTL expired messages.

If you can see your router (which is a different address from your PC, right?), then it's probably not ZoneAlarm causing the problems, but more likely your router - or your ISP.

You might do some Google searches on your router brand and model number along with "ICMP", "PING" and/or "TRACERT" to see if there is any information out there on this. I did a quick search on this and it looks like your hardware probably supports ICMP - although it may not be configured (I didn't get far enough in to this to check it, but that's a possibility).

You should also try doing a search on your ISP with the same terms - to see if people are noticing problems with your ISP. Due to the worm/virus/trojan attacks we've had recently, many ISPs have started blocking or restricting ICMP echo requests - a call to your ISP's support department might be able to help with this too.

No answers here - just some ideas.