Daniel,
Thanks for your reply.
Pings to 127.0.0.1 as well as 192.168.3.11 (its local ip address) work fine, as do pings from this box to another. It's pings to this box from another that fail:
Reply from 192.168.3.11: bytes=32 time<1ms TTL=64
Reply from 192.168.3.11: bytes=32 time<1ms TTL=64
Request timed out.
Request timed out.
Request timed out.
Reply from 192.168.3.11: bytes=32 time<1ms TTL=64
The Remote Desktop issue is strange, because it won't connect, won't connect, then it does connect, but drops. I think it has to be a networking issue, most likely the NIC, but I'm not sure what to check.
John