There are two steps to adding drivers to a WinPE image. The first is the obvious step of adding the drivers, which need to be added as INF, CAT and SYS files plus any support DLLs (and not in EXE format).
Once added, the drivers then need to be selected before you create a new WinPE boot image.
If you are unsure that you have the correct drivers for your NIC, create a WinPE bootable USB device, and add the drivers to a folder on the USB device. Boot WinPE from the USB device and exit to a command prompt. Locate the drive letter that the USB device is mounted on, change directory to the folder containing your driver files and type DRVLOAD <full path to driver INF file>
A successful driver load will be reported at the command line. You can then try doing an IPCONFIG /release and IPCONFIG /renew and see if that all works.