Windows 7 Strange Network Issue (Completely Stumped)

I am running Windows 7 Professional on a desktop computer and Windows 7 Home Premium on a laptop. They both can successfully connect to the internet without a problem. The laptop connects through wireless and the desktop connects through a wired connection. These two computers, however, cannot communicate with one another. I am able to see both of them in the Network and HomeGroup, but I cannot access either of them. When trying to access either of them from the Network I receive the simple message that "Windows cannot access \\(computer name)", so I diagnose the issue. This is where things become different.

If I diagnose why I cannot access the laptop from the desktop computer I get the message "Your computer appears to be correctly configured, but the device or resource (Laptop) is not responding." If I diagnose why I cannot access the desktop computer from the laptop I get the message "File and print sharing resource (Desktop) is online but isn't responding to connection attempts." I should also note that I can ping the laptop from the desktop, but I cannot ping the desktop from the laptop.

Incidentally, there are two other computers on this network as well. One is a laptop let's call Laptop2 that runs Windows 7 Home Premium and the other is a desktop we'll call Desktop2 that runs Windows XP. They both connect wirelessly and have internet. They are a part of this concern only because Laptop can see and access these other two computers but Desktop cannot even see them. Laptop2 and Desktop2 can access Laptop, as well. This leads me to believe that the issue I'm having mainly lies with the Desktop, but I'm completely stumped. Why can't these two computers (Laptop and Desktop) communicate with each other and even more, why can't Desktop even see the other two computers?