Sorry for taking a few days to get back. This system is a somewhat older Intel dual socket server board, so I wasn't sure I'd find the setting you suggested. I did not see anything resembling "QuickBoot" or "FullBoot".
The kernel that does work is 4.8.6. The other two are 4.9.10 and 4.10.14, both of which just show a black screen. The display doesn't turn off, it's just an all black screen with nothing on it. I tried removing the quiet and rhgb options, but it still does the same thing. None of the keys do anything, and I have to hard reset.
I have been attempting to go through the journalctl logs, hoping to find the point where it tried to boot one of the two kernels that don't work, but I am not successful thus far. I am still trying to learn how to go through these logs. This site has been quite helpful: link