So I bought a new (old) Mac Pro; late 2009, 12/24 core, 64GB, NVIDIA GeForce GT 120 512 MB. It’s running macOS 10.12.3 Sierra. I hooked up one monitor to the HDMI port, and one to the DVI port. Seemed to work fine.
Until I rebooted the machine.
Then it refused to show the mouse pointer (Apple magic mouse), although It would warn of the mouse’s disconnect and reconnect if I powered the mouse up and down. Likewise, there was no response to the keyboard. It just sat there showing login options for me and a guest; it wouldn’t respond to anything at all I did with mouse or keyboard.
After trying power downs, pulling the plug for a while, pounding on the keyboard, powering the mouse up and down, I finally thought to pull a connection to a monitor. Specifically, the DVI-connected monitor. Immediately the mouse pointer showed up, and I was able to log in.
Up to this point, I had the machine set up so that the HDMI monitor was on the left, and was my home (boot screen) monitor. That’s the one you drag the menu bar to in the Prefs / Displays panel. But I noticed when the machine booted, it showed up on the DVI monitor first, then the HDMI monitor, and then it locked up.
So, still booted up after all this screwing around, I swapped monitor cables, then set the DVI monitor to be the home monitor, as the left monitor was now my DVI-connected monitor instead of my HDMI-connected monitor.
Now the machine restarts cleanly, or at least, it has a few times in a row.
So if you’re having this kind of problem, after the login screen shows, try pulling one or the other or both of the monitor cables to see if it will unlock the mess. And make sure the DVI monitor is your home monitor once you get things running again.