I have spent many hours and read many posts about this problem and finally have some evidence that Windows Firewall is the problem. Here's how I know:
The only way I can ping the computer is to stop the firewall service and change the service startup from "automatic" to "disable." Then, only after rebooting the computer, I can finally ping it. I can still ping it even after I manually restart the firewall service and turn the firewall on. But if I reset the service startup to "automatic" and reboot the computer I can't ping anymore. Something gets hosed up during automatic startup. Any ideas are greatly appreciated, but keep in mind that I have tried all basic solutions, i.e. setting firewall rules, allowing incoming echo requests, network name, network and file sharing is on, etc.