Since 10.0.0.0 is the reserved Class A private subnet, I would expect your router and linux box configured themselves with the default mask 255.0.0.0 unless you actually set it to 255.255.255.0
You can use the arp command to find out whether the other devices 'see' the ip/MAC for your shield.
And WireShark can be invaluable as a tool to watch the actual traffic over your ethernet segment. Download it from wireshark.org. I keep an old laptop around with it installed for whenever I have such connectivity issues.