I had a similar issue, after completing our Windows 10 deployment it would sit on the local admin desktop and fail to continue to install anything more than the OS itself.
I rebuilt an entire new image, straight from an ISO from Volume Licensing site, installed all updates etc, and then created a unattend.xml by following the first section of this GUIDE under the ADK bit.
After this, my unattend file works perfectly and the task sequence handles the rest within MDT. My applications now install, the only thing I have different compared to my Windows 7 deployments is that I don't attach any profile to install drivers or packages under the task sequence.
Hope you've sorted it by now, let me know if you need anything more explaining.