I found that PCI cards sometimes are more "quirky" than non-PCI cards.

Can't tell anymore how often a PCI card at first didn't work simply because it was fitted too tight or was fitted with some tension (fore or aft) in the System.

I would recommend :
- clean PCI connectors (both card and Slot)
- test the card without fixing it (to excert no additional pressure into the slot)
- have the PCI connectors of the card remain visible for about 1mm
- avoid any tension on the card's connector in the slot
- if all else fails : move PCI card to lower slots
- if even that fails : switch PCI latency to 32 or 64

Weird enough, I keep seeing such problems being solved by that in my Network (operating 22 PCI Cards). Can't tell exactly what the cause is, but the fixes - born from years of Trial&Error usually do the trick.
Anyway, because a System isn't booting from a PCI card doesn't mean anything to me anymore, as in almost all cases I ever saw the Boards/PCI VGA combination could be made at least work to display an image or get into the BIOS.

Does the same occur when going into the BIOS or booting into a Low-Resolution Safe Mode ?

Weird, isn't it ?

I have never found out why this phenomenon occurs, I only know that this workaround helps in most cases.
Never had any comparable issues on AGP or PCIe slots...