Each of your computers should be set with the exactly the same Workgroup name.
Start> System> Computer name> Change
But each computer should have its own unique name. Keep all the names short (for ease of future network drive mapping).
"Network Place" does occasionally not show what is connected reliably, especially when they are swapped in and out of the network. (hence the use of network drive mapping)
I presume you haven't set up any security on your network? Encryption, MAC address filtering, etc?