So if you plug direct onto the ZD with your laptop can you ping it then? if not it have you tried to see if it has defaulted to the default IP address is believe is 192.168.0.2 admin admin. If that doesn't work you could try the factory reset, hop...
Just to confirm. Your laptops in the same vlan and you can ping all AP's and the ZD. Also you have rebooted at least 1 AP and the ZD. If so i would look at using putty to ssh into an AP
Do you have any AP's connected onto the same switch as the ZD1200. Also are there any VLAN's in place? Has anything changed on your network? and looking at the logs did they all go offline at the same time?