Ok, I'm going to stick my neck out here and say that your problem
IS ZoneAlarm
I'm prepared to bet that ZoneAlarm is interfering with the DHCP lease process which is preventing your machine from correctly re-indentifying itself to the network.
Start > Run
cmd
ipconfig /all
There should be an entry in the list that pops up that lists your connection and IP details, one of the items listed
should be your DHCP lease expiry date/time. Can you tell me what this is set to? Or at least see if it seems like quite a short time?
The next time your computer stops responding
should be on, or around, this time.
If that's the case it's ZoneAlarm and we need to get it configured so that it allows the lease process to work properly.
(ooooh, I'm gonna regret sounding so confident

)
__________________
By the way, the previous advice about changing over to Ethernet (rather than USB) is
good advice
I would say that you should do this if you can, regardless of whether it solves the problem or not

__________________
Oh, by the way.....
I
am right in thinking that ipconfig /all will show the DHCP lease expiry aren't I?
It doesn't on mine, but I think that's because I've got a fixed IP through a router