Link-Local Connection to Device Not Working

It appears your network settings are mis-configured. RGS's comment is correct: by selecting a local link, you are ensuring a network connection will not work. The IP address you've displayed that automatically works, is in the APIPA range. This is not the drone you seek...I mean connection.
http://packetlife.net/blog/2008/sep/24/169-254-0-0-addresses-explained/

All you should need to do for a wired connection is plug it into the computer; Ubuntu does the rest. https://help.ubuntu.com/12.10/ubuntu-help/net-wired-connect.html

If you are trying to connect 2 computers directly to each other, I would recommend assigning a "static IP address" to the Ubuntu machine: https://help.ubuntu.com/12.10/ubuntu-help/net-manual.html
In that case, give the Ubuntu Machine the following settings:

IP Address: 169.254.146.89
Subnet Mask: 255.255.0.0
Default Gateway: 169.254.146.88 (or whatever it says for IP Address in the window of that print screen you posted, the point being for it to find the windows machine by it's IP Address)

To access your network settings:

1. From the Dash Home (Ubuntu start menu, also accessed by hitting the windows key)
   type network and hit Enter.
2. Select Wired/Wireless and turn it On.

You listed some very detailed information, which is good. You did not give enough basic information though, such as:

1. How you are connecting: via a router, switch, modem, or directly to another computer.
2. Your desired network setup: DHCP, static, APIPA.
3. How many and what kind of devices you want to connect.

Ubuntu has some documentation aimed at walking you through setup. Please read that before posting a question in the future. https://help.ubuntu.com/12.10/ubuntu-help/index.html