Hi Johsp,
Essentially, the BIOS should not have anything to do with the NIC Card detection. The BIOS is just to bootstrap the system. From the looks of it, what has changed in the two motherboards are the integrated NIC cards and/or drivers/firmware.
The older set of boards worked "out of the box" with respect to the the NIC cards which is not happening with respect to the newer boards.
There are two ways to get over this:
1. Temporarily use a "supported" - (basically, "detected") PCI NIC card on the new hosts and install ESXi - it will allow you to do the install once it detects the NIC cards. After installation, you can then check and install the required drivers that the hardware requires and once that is done, the add-on NICS can be removed
2. Check the exact hardware of the NIC cards and build a custom ESXi ISO using something called an "Image Builder" that you can manually "inject" the required drivers on, So essentially, you take the default ESXi image, customize the image and inject the drivers. Once that is done, create an ISO out of that, and boot and install ESXi on the new hardware.
The below link should help with "Image Builder"
Image Builder Overview
If you ask me, the easier option would be to be a couple of cheap "over the counter" Intel based E1000 NIC cards which should allow installation to proceed.
VMware Compatibility Guide: I/O Device Search
Regards
a