I have been using the TX1 and had no issues running some of the sample code. However, I was in the middle of installing openCV and it was crashing. I hit the reset button on the TX1 board and now when I try to boot it up, it gets stuck on the desktop background screen.
Do you mean the NVIDIA logo? If so, then it is stuck in early boot stages. One of the best tools to see what is going on in that case would be serial console. See:
http://www.jetsonhacks.com/2015/12/01/serial-console-nvidia-jetson-tx1/
Note that if you put the Jetson in recovery mode it won’t actually do anything other than put it in a mode the driver package understands. If you put it in recovery mode with the provided micro-B USB cable connected to your host PC, then the TX1 should show up with:
lsusb -d 0955:7721
…if this shows up you know at least that some basic part of the Jetson is still alive and perhaps flashing would make up for the problem. This would also allow you to clone the rootfs in case it is still intact and there is something you want to save.