PCIe SATA multiplepler card not detected

[Álex]

To use an external JBOD box I have this multiplexing eSATA PCIe card (Startech part PEXESATA2):

https://www.startech.com/eu/Cards-Adapters/HDD-Controllers/SATA-Cards/2-Port-PCI-Express-eSATA-Contr...

I have been using it in two different computers in the past without issue. Now, in this new HP box the card is not detected at all neither in the slots #3 nor #4 (#1 is used by the GPU, #2 untested because it was close to the gpu).

By undetected I mean that it does not show at all in the PCI bus, according e.g. to lshw in Linux:

$ lspci -tv

-[0000:00]-+-00.0 Intel Corporation Sky Lake Host Bridge/DRAM Registers
+-01.0-[01]--+-00.0 NVIDIA Corporation GK208 [GeForce GT 730]
| \-00.1 NVIDIA Corporation GK208 HDMI/DP Audio Controller
+-02.0 Intel Corporation Sky Lake Integrated Graphics
+-14.0 Intel Corporation Sunrise Point-H USB 3.0 xHCI Controller
+-14.2 Intel Corporation Sunrise Point-H Thermal subsystem
+-16.0 Intel Corporation Sunrise Point-H CSME HECI #1
+-16.3 Intel Corporation Sunrise Point-H KT Redirection
+-17.0 Intel Corporation Sunrise Point-H SATA controller [AHCI mode]
+-1f.0 Intel Corporation Sunrise Point-H LPC Controller
+-1f.2 Intel Corporation Sunrise Point-H PMC
+-1f.3 Intel Corporation Sunrise Point-H HD Audio
+-1f.4 Intel Corporation Sunrise Point-H SMBus
\-1f.6 Intel Corporation Ethernet Connection (2) I219-LM

I have tried disabling and enabling the PCIe slot in the BIOS with no difference. 

Is there any reason why the card wouldn't be detected at all in this model's motherboard?

Thank you in advance for any help.