<<<Having tried "ipconfig" and "ping" sucessfully, I am baffled>>>
"ipconfig", depending on the switch used with it (ipconfig /all) just displays the details which may not necessarily be correct.
/release will release current addresses and should set to 0.0.0.0
/renew should force a renewal of the addresses from an available DHCP server, unless a fixed IP has been allocated.
Similarly being able to 'ping' other PCs on the network doesn't necessarily mean they are all set up correctly.
What IP addresses do the three PCs in the network have?
If you have enabled "Internet Connection Sharing" in a Host PC, this should have the fixed IP address 192.168.0.1 subnet 255.255.255.0 and it should allocate addresses in the same 192.168.0.xxx range to the Client PCs.
If you are not using "ICS", then you need to allocate fixed IP addresses in the correct range to each of the PCs.