VMware ESXi 4.0 doesn’t support Realtek RTL8111/8168 network cards by default. When you try to install ESXi on a computer with a Realtek NIC it will say the network card is not supported and will not allow you to proceed with the installation. Luckily you can modify the ESXi ISO to include the Realtek driver so that you’ll be able to install it without a problem. A forum post describes how to do this. I’m echoing the steps below.
Create a folder and copy your VMware ESXi ISO file
Download RTL8111_8168_P55_integr_SATA_Ctrl.(AHCI).oem.tgz and copy it to the folder you just created
Run sudo ./mkesxiaio_3.9.sh
Burn the modified ISO
Realtek network cards are not exactly esoteric hardware. Not sure why the default installation doesn’t have support for this. If you’re trying to install ESXi better check the HCL.