Usb wireless device problem
can a cricket wireless usb device cause a computer to shut down completely
Pretty unlikely. It won't need more power than a USB port can provide but even if it contributed to drawing too much power by being plugged in with other USB devices, it would only block that port and not the whole system.
What's actually happening to the system when it shuts down? Look at the Event Viewer in Control Panel>Administative Tools when you restart, to see what went on.