I got my Mac Pro back from Apple the 3rd time, and this time it wouldn't boot at all. My screen would turn on, but clearly wasn't getting a signal. I was unable to reset NVRAM, or get into safe mode as the machine was completely unresponsive and stuck somewhere between the boot chime and the login screen.
Oddly, plugging the display into any other machine was fine but the real issue ended up being similar to yours. It is my Thunderbolt display. For some reason a machine that was already booted had no issues right away, but any machine plugged into that monitor during a boot (reset, or a power on) had the exact same issue as my Mac Pro. I'm sure that is why I never witnessed issues on my Mac Book with this display, because well... I never turn it off.
Apple said that it could be a faulty cable, or the logic board inside of the Thunderbolt display causing the issues. It seems like this is not a common issue, and it can take a while for it to consistently cause issues. The engineers I worked with had never seen or heard of this issue, but their eyes lit up when I was able to demonstrate with my machine and theirs. Up until this point, it was locking my Mac Pro up, and making it boot loop. I have that display in for repair now, and my Mac Pro has been running like a champion for two days without it.
One more note that probably should have been indicator for me a few weeks back. While plugging in the thunderbolt cable to my MacBook, I saw a small flicker / spark on the signal plug when the cord touched the aluminum on my MacBook. I thought I was seeing things, but that probably isn't right.
I hope all of my pain and suffering can help someone else
Allusis I am actually not that surprised given our office's experiences with the Thunderbolt displays. As they have aged they have failed in interesting ways. Most, if not all, at this point have cracked cables just beyond the cable strain relief on the thunderbolt plug in. We have been wrapping the ones that still function with silicon tape to protect them and add more strain relief. We have also had displays that fail to show up immediately, causing delays after boot. Others also need several reboot cycles to come on consistently. Our office is in the middle of a MacBook Pro refresh (so far about 1/3 replaced with 2016 MBPtb) that are now using the usb-c to thunderbolt adapters which add a whole another layer of complexity and new interesting fail modes. The are older displays, bought when they first came out, but I think we have had about a 20% complete failure rate since that time, with other limping along. As we are replacing laptops we are looking at new solutions, but Apple's exit from the display market has made that search "interesting".