How cheap could a .NETMF board be w/Ethernet
Setting aside the .NETMF for a second, you are essentially asking for a single board computer with Ethernet. Cost is directly related to the number of units you plan to produce. Cellphones are so cheap because they are made in the millions. If you only make one or two of something it can be orders of magnitude more expensive.

As was pointed out in the comments, the Netduino plus at $60 retail quantity one is certainly an upper bound on cost. 

The Rasberry PI at $35 retail (model with Ethernet), while not supporting .NETMF, does have an ARM processor with sufficient memory so in theory at least one could port the .NETMF to this device.

As to 5-10 dollars, that is extremely ambitious, you would need extremely high volumes. Of course remember Moore's law (costs drop in half roughly every 18 months) so if you wait long enough you may see a $10 board running the .NETMF.