Well, in that case, your card is very likely fried, or at least, the fuse kicked in and turned off the card electrically.
Look at the card very carefully - see if you can find a feature (specifically an SMT fuse) that starts with the letter F (F2 on my ConnectX-3, might be F4 on the ConnectX-4). On each leg of the fuse there is usually a pin hole (that's the FNP mentioned by
@Freebsd1976). Grab a multimeter, put it on continuity mode, and put one test lead on each side (to see if current is moving across the fuse). If it doesn't beep, then the fuse has blown. You'll likely need to borrow a magnifying glass to read the code off the fuse. If you can solder SMT parts, you might be able to look for a replacement fuse on mouser/digikey and swap it out. Or take advantage of the 2 pin-holes and solder in something that can act as a fuse.
If it beeps, well, you'll have to get a bench power supply, feed 12v into the PCIe power pin and troubleshoot the power plane with a multimeter. Depending on the time investment it might not be worth the hassle.