I updated to 2.0. printed a calibration cube. removed the print and sent the head to X150 Y150 Z10 ( 10mm above the center of my bed) and this is the result...
https://gyazo.com/384ec6ddfaa195b510a2755408a18a8c
No more strange offset after a print!
Thanks to everyone for all the help and tips!
@dc42 So I wanted to wait until I tried all avenues before filling out a warranty claim. I ordered brand new 32gb card ( my original one was a 64GB that I partitioned to a 32GB and I reformatted/ re partitioned it multiple times during the diagnosis and I could see the card just fine on my PC so I assumed it couldn't be the card.) I put all my files on the new card, installed it on the board and Viola!
I have power cycled the board multiple times and the wifi connects every time.
I'm sorry to have gone through all of this only for it to be an apparently bad SD card. I very much appreciate the time you took to help me out though, especially during the holiday season. Hope you had a great holiday and thanks again!
I bought mine through Filastruder so I guess ill have to shoot them a message and let them know?
If that's what you recommend at this point I will gladly accept. I love my duet but this issue is truly baffling. How would I go about doing a warranty claim?
It does work on a charger. I have noticed that the Wifi module doesn't always turn on, ( maybe 85% of the time it does first try, it usually works the second time you power it on. ) but it never automatically turns on with Vin power. I did go through all the caps from the diagram that would control power to the Wifi and USB and I could not find any shorts to ground. I also couldn't find any issues with any of the diodes in said circuits. This is, indeed a puzzling fault and a bad time for it to happen as well because I need my printer to print the final parts for my other printer 
M111 command shows debugging enabled for no modules. I am using YAT but I don't know what you mean about does it display anything received from the USB port.
I do not have an M111 command in config.g . Nothing was done to the board/ config prior to this issue appearing. The only thing that I noticed was that occasionally DWC would load a bit slow but it was never a major issue.
I verified that the +3.3v rail is present with both Vin and USB power. If I plug in the USB, the Wifi turns on and connects. I am able to load the DWC page and make changes. If I unplug USB and go to Vin the wifi does not turn on. I am so baffled as to what the issue could be. I am ok with basic electronics and soldering but this is just throwing me for a loop.
As the title says, my Duet Wifi will only connect when there is a USB cable powering the board and will not work when just powering on through Vin. I have tried updating the FW, completely reformatting the SD card, different DWC, different wifiserver. The only physical issue I could find was a cold, loose solder joint on one off the Vin pins. I fixed that but it didn't change anything. When I did get the wifi to connect if I type in the IP I get a page that says "your Duet rejected the HTTP request: page not found." When I first got that is when I reformatted the SD and changed the www folder to -old and made a new one, which made no difference. I am starting to think that maybe the issue might be something with the board that I cant easily see by eye.
Any help would be greatly appreciated.
I updated to 2.0. printed a calibration cube. removed the print and sent the head to X150 Y150 Z10 ( 10mm above the center of my bed) and this is the result...
https://gyazo.com/384ec6ddfaa195b510a2755408a18a8c
No more strange offset after a print!
Thanks to everyone for all the help and tips!
@phaedrux that's possible. I'm running dual leadscrew steppers for my Z so I didn't think it could be that but it's definitely not out of the realm of possibility.