I am unclear about the question.
The ISA server itself (192.168.1.1 on one NIC, 192.168.0.1 on the other) can ping its own IP addresses.
Clients (192.168.0.2, for example) can ping 192.168.0.1.
Perhaps if you try tracert instead of ping you will see your answer.
192.168.x..x is typically a class ‘c’ address, which gives it the mask of 255.255.255.0 (Typically), you can subnet that into any subnetmask that works best for your organization, but based solely on the limited info here, my initial guess is you have two different networks and while Salam is correct, the ISA server can always ping it’s on periferals, your clients won’t be able to unless the overall network is configured that way through the use of a switch or router.
I don’t know if this helps, but from what I can tell that’s what it looks like initially.
Also, along teh differing network lines, your gateway might need to be different on teh switch pointing traffic towards the server and not the ISP router’s gateway. Those should be different I believe.