It all depends if any of the power trases to the blank slots are active and where they make contact to the pins of the PCI slot. If the power is on on of the inner layers of the board it will be next to imposible for you to get it solderd. Not to mention if you use too much heat you could damage the board. I suggest finding an alternate way of powering the card.

I suggest looking up the pinout of a PCI slot to ID what voltages are on what pins. Then ID the pins in use by the card. Then run wires from the PSU to a PCI slot or dirrectly to the card and your all set.