Yes I can ping the local NIC.I can also ping to another local Windows ME machine.
I can't ping the E-Smith private server/gateway on 192.168.0.1, but I can still use use it with no problems, both as a file server and as a gateway (dial-up modem).
Using SSH to E-Smith I can see that E-Smith can ping addresses (numerical or text forms) on the internet.
I can't ping the same addresses from the Windows ME machines.
This is not too much of a problem, but it would be good to understand what's happening here.