It's been a really long time since I dabbled with this (I last flashed a Radeon 9600 for my PowerMac G5 in like 2012), but in my experience unflashed cards almost never worked reliably. If you have access to a machine which can be used to flash the cards, it's a pretty straightforward process and I believe you can (and should!) back up the original card flash to make sure that anything you do can be reverted.
I found a good [link|https://blog.greggant.com/posts/2018/05/07/definitive-mac-pro-upgrade-guide.html#efi-flashable|list of flashable cards here|new_window=true], it looks like only the Radeon 2600XT and 5870 are flashable in a way that will get you a boot screen. What I'm reading suggests that most non-flashed ATI cards should eventually give you a video output IF MacOS can successfully load the driver, which is a big if depending on how the cards identify themself.
Your best bet for a reliable setup would be to flash one of the ATI cards, though there may be some underlying problems with your macOS install that are preventing drivers from loading. If you can, try doing a clean OS install to a different hard drive which will remedy any issues caused by the old installation, it's possible the previous owner mucked things up while trying to get the GeForce 8400 working.