I can confirm a similar experience.
I was having mutilple, seemingly random blue screens (BSOD) on a new Windows 7 Home Premium 64 bit desktop with Zone Alarm ES installed.
I was receiving frequent BSODs with stop error UNEXPECTED_KERNEL_MODE_TRAP (7f) alternating with stop error DRIVER_POWER_STATE_FAILURE (9f).
In the case of the UNEXPECTED_KERNEL_MODE_TRAP (7f) the Windows Debugger seemed to indicate a probelm with NETIO.SYS
In the case of the DRIVER_POWER_STATE_FAILURE (9f) WinDbg indicated an issue with Rt64win7.sys , which is the driver for my REALTEK PCIe GBE Family Network Controller (NIC).
I checked, and the drivers for the REALTEK NIC seem to be up to date.
The remedy I found was to completely uninstall Zone Alarm.
Since uninstalling Zone Alarm, I have not experienced another BSOD.