Rock solid here on two systems. (The third, being in storage pending a rebuild to Linux, doesn't count).
Of course, I have a Smoothwall firewall between me and the Internet. And my W2K server runs Outpost behind that.
And immediately downloading and installing ZoneAlarm is no good. Chances are you're already infected. Download on another machine, burn to CD, install XP on target, install ZoneAlarm, then connect target to internet. Either that or slipstream XP SP2 into your install set (note that I have yet to do this).
Failing that, it'll be a harware issue. If it uses a VIA chipset, have the Hyperion drivers been installed? Is there any hardware not on the HCL?