Arduino Due and Wifi Shield 101 compatible?

So I'm trying to do a project where I have a thermistor sensor that displays the temperature and humidity on an LCD screen. I have the code running and that works fine. Now I'm trying to add the Wi-Fi shield to it to transmit this same data wirelessly to my computer. I've connected the shield to the Arduino Due and when plugged in the LED on the shield shows it has power. The other three leds that indicate wireless connection, wireless connections available and error do not light up. I would assume that at least one of the three would light up. We have multiple wireless connections in our area including encrypted and unencrypted. Are the Arduino Due and wifi shield 101 even compatible? If not is there another way? I know there is ethernet but can someone explain that or any other choices?

I've not used the Wi-Fi Shield 101 but if it behaves similar to an ESP8266 Wi-Fi module then I may be able to point you in the right direction.

Firstly, what do you mean by "transmit the data to my computer"? What, exactly, are you trying to achieve here? Do you understand how web servers work in serving up (but not actually transmitting) web pages?

If you were using an ESP8266, for example, that would be the web server; your computer (or any other device on the same network) could request a web page (or just the data) from the ESP8266 but there would be no "transmitting of data" in the sense I believe you mean! Think of how the Internet works. Google doesn't transmit anything, you just go and get the data, right?

Describe, step by step, what you are trying to achieve or expect to happen - that way your understanding can be corrected if necessary or others can assist you in achieving your goal.

Just as an aside, in case your terminology is off course, you can transmit data using, say, a 433Mhz transmitter and receive that data on your computer (well, actually by the matching receiver, and then do something with that data, potentially on your computer). Perhaps you mean this?

The temperature and humidity data is to be sent to my computer and will update a .csv file which will graph the data. I'm not too worried about all of that right now. Right now I need to get the Wi-Fi shield connected. Do you have the schematic for how its wired to the Due? I've looked everywhere and can't find anything besides having it attached directly to the board.