After searching high and low for an answer to this same problem I was having with my Kindle 3 I have solved the problem.
The problem is that to establish a wifi connection the Kindle3 does a probe of
http://spectrum.s3.amazonaws.com/kin.../wifistub.html
and expects to get back:
81ce4465-7167-4dcb-835b-dcc9e44c112a
If it doesn't it won't let the kindle3 connect to the wifi you're trying to connect to.
Here's how to solve the problem.
Jailbreak the Kindle3
Establish an ssh session to the kindle3
Go to this directory on the Kindle3: /etc/kdb.src/luigi/system/daemon/pmond/wifid/
Modify this file: start_cmd
Change this line: /usr/sbin/wifid -f
To this: /usr/sbin/wifid -f -n
and save the file.
Restart your Kindle3 and try connecting to your local wifi router that is set up for local access only.
It worked for me. I thought I would share this since I couldn't find it clearly laid out anywhere else.