Ah. I had the issue were the fan wouldn't spin because the ulps setting needed to be disabled. Its some power saving mode and the card doesn't look like its works but the computer see it. That was my case. If it put a load to the card the fan you start to spin. Since your rig does recognize the 3rd card in devices I would put the 3rd card in the 2nd card slot and see if it works. That will have you narrow down the issue
Ulps is a registry setting. I don't think it exists in linux, but regardless, the 3rd card does not spin up before the operating system is loaded. I believe all the cards should power on when they are recognized by the motherboard POST, right?