No worries...
That looks like a Power Mac G5 (Late 2004). If so, the default graphics card slot is the 8x AGP Pro bottom slot in your picture. The other three slots are 64-bit PCI (33 MHz) or PCI-X (100/133 MHz), depending on the exact model. If you have 4 RAM DIMM slots, they are PCI, if you have 8, they are PCI-X.
If that is correct, let me know. If you can let me know what cards are installed and in what slots top to bottom, we may be able to figure something out. The top card in you photo could be moved to the slot with the damaged pin, since it doesn't use that part of the PCI connector (if the damaged pin is where the yellow arrow is pointing)
C