Actually, honestly you should just go walmart or BestBuy or something and buy a wifi bridge, or router or something - something that connect to a wired network and act as an AP (Access point)
That way, you can connect over Ethernet on 192.168.0.100 and use the web config thing and configure Wifi that way, once that's done your avalon will have two IPs, one for the ethernet port (eth0) and one for the wifi adapter (wlan0). Once that's done your Avalon should be able to connect to the internet.
A wifi AP is like $20-30, way less then 1BTC. If you buy one and it works, you can subtract that from my bounty
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I think you might be able get it to get an IP address from your router by configuring it to act as a DHCP client (under Network/Interfaces/Lan - protocol pulldown), but the problem is once you get a address lease, you won't know what the IP address is of your Avalon, and won't be able to connect to it over the web, unless you can get that information from your router somehow (it should be possible to see that information
somewhere but each router is different. Normally when I'm setting up a network thing, I'm using a keyboard and monitor, not doing it over the network itself, with no other way to connect to the device!)
Other then that, you could try leaving your IP static as 192.168.0.100, but setting the gateway manually on that same page (Network/Interfaces/Lan)
On your windows machine run the command 'ipconfig' in the command line. Look for he line that says "Default Gateway". There should be an IP address.
Plug that IP address into the gateway field on the LAN setup tab.
After that's done, you can check to see if you're connected to the internet by going to the Network | Diagnostics tab and trying the ping tool
One thing to keep in mind, though - you want to setup your cgminer config stuff right away. If you get online before setting that stuff up, you'll automatically start mining using the preconfigured pools, and making money for Avalon!