Thanks for the advice. Tried it, didn't work. Here are some of the messages I get:
When I go to Control Panel > All Control Panel Items > Network and Sharing Center, and click on the "Network" icon in between my laptop icon and the internet icon, I get a popup which shows both the laptop icon with the right name, and the desktop icon with the right name. When I double-click on the desktop computer icon, I get the message "Windows cannot access \\COMPUTERNAME" The error code says "The network path was not found."
Another thing I've tried is right-clicking on the desktop computer icon and trying to Connect with Remote Desktop Connection. When I do this, it searches for a few seconds to find the connection and then I get the message "Remote Desktop cannot find the computer \\COMPUTERNAME. This might mean that \\COMPUTERNAME does not belong to the specified network. Verify the computer name and domain that you are trying to connect to."
Is it possible that I have two different networks operating here? That was always really easy to see when in Vista or XP, but not in 7. How would I find out?
Thanks for advice!!