I had this working for years but now it's broken and I'm not sure how to fix it. 5,1, Mohave, Gigabyte RX680GAMING were all working great. But I had to do a fresh install of the OS and now I can't get any display. I have tried:
* Booting in recovery mode
* Booting to Open Firmware
There is no Open Firmware with Intel Macs, the last Mac with Open Firmware was the Power Mac G5.
This doesn't even make sense since at least 2007, there is no PRAM with modern Intel Macs - MacPro4,1/5,1 have a SPI flash memory to act as a NVRAM volume and store settings/configuration parameters - and you can't literally flash anything to the NVRAM, you can only reset it (via a completely different process from the PRAM, where the non volatile data is erased from the SPI flash memory) or bypass it temporarily.
Seems you are using long obsolete technical terms from the PowerPC era that do not directly apply to a Mac Pro.
* Replacing PRAM battery and flasdhing it again
The BR2032 battery function is to keep the RealTimeClock controller powered while the Mac Pro is disconnected from power/deep sleeping/etc.
While the RTC controller have a battery backed SRAM internally, this tiny memory (around 512 bytes) is used exclusively for RTC related variables/counters that need to be constantly updated like timesinceboot and is nothing similar to an Open Firmware PRAM where general configuration data was stored in a battery powered SRAM.
MacPro4,1/5,1 have a completely different design from Power Macs and nothing applies directly here.
* Reseating video card
* Booting with a different video card (all I had was a "3D Force FX-5200LE 128M" but it didn't work
* Multiple monitors, cables, and keyboards
No matter what, I get a chime but no display. (Even if I wait 20 minutes) If I plug the keyboard in I see caps lock flash green but that's it. If I press caps lock, nothing happens. Nothing happens if I hit eject. Dual Xeon X5690 64GB RAM. Thanks.
Install a confirmed working GPU and a disk with a working/supported macOS install, remove everything else. Now remove the RTC battery from the backplane battery holder and power on, this procedure will instruct the Mac Pro EFI firmware to temporarily bypass the NVRAM and enter a fail-safe mode. If you now can finally boot, you will need a BootROM reconstruction service.
Doing anything besides that will be literally useless for the diagnostics.