No experience with this hardware, but know a bit about configuring networks, and seem to recognise some problems from experience with 1541 Ultimate

First i need to know if you are using a HUB or a Router ? Did you have DNS enabled on your router ?
when using a hub, a DNS server is probably not reachable, and therefore maybe the device won't work with contiki.
When you are using a Ethernet Cross-Cable, same problem, no DNS resolving, Contiki won't work.
If you are using a router with DNS (forwarding) support, set your DNS for your Commodore device to the router, not to the GateWay for your ISP ! The router will try to resolve the request locally first, then forward it to it's parent DNS server if configured correctly.
Before using Contiki try to configure it right, and download the entire D64 image, instead of just the CFG.
I advise you to read my 1541 Ultimate Guide regarding Ethernet support, it might very well help you with getting a working setup for your own (non 1541U based) setup.
Do a 'IPCONFIG /ALL' on your PC to get the IP for your PC, NETMASK, and DNS Servers for your NETWORK, and GATEWAY for your PC. If you are using dynamic IP i.c.m. with a router, your GATEWAY and DNS SERVER should beat least identical to the LAN IP of your router. Remember that all MAC ADDRESSES and IP ADRESSES need to be unique on your LAN.
Use the same values of your PC for your C64, but choose a different IP ADDRESS. Be sure that your MAC ADDRESS is unique. IP addresses are LAN based (192.168.x.x , 10.0.0.x, and a third i can't remember), or internet based (all other addresses but the ones mentioned in the before ranges are considered non-lan), but MAC addresses also need to be unique. First a MAC is resolved to an IP ADDRESS, then the IP ADDRESS is used to deliver information. When there are 2 exactly the same MACS reachable from a specific host (local network or internet for that matter), it leads to trouble because a receiving NIC can no longer be uniquely identified.
There are special addresses and reserved masks, keep that in mind.
A common reserved IP address is 127.0.0.1 (local loopback) and any IP address ending of which last digits are 0.
A common network mask is: 255.255.255.0 (for the 192.168.x.x/127.0.0.x networks) and 255.255.0.0. (for the 10.0.0.x network)
Avoid any IP ending in 255 (as it is mostly the broadcast address) and avoid any IP ending in 0 (as it is mostly considered to be the network), and avoid any starting with 127 as it might be the local loopback.
Perhaps this helps.