I'm assuming you are able to get into WindowsPE, but it doesn't get an IP address to connect to the Core Server? I don't have any experience with that machine personally, but I was able to find these links for "driver packs" from HP:
http://ftp.hp.com/pub/caps-softpaq/cmit/HP_Driverpack_Matrix_x86.html
and
http://ftp.hp.com/pub/caps-softpaq/cmit/HP_Driverpack_Matrix_x64.html
The 1040 G1 appears to have x86 and x64 drivers for Win7 and Win8.1. If you are in UEFI, then it should be loading the x64 WinPE, so you will need Windows 8 x64 drivers. You can try the Win8.1 drivers.
Looking at information on the 1040 G1, it looks like there isn't an RJ45 connector on the machine, but it requires a dongle/adapter or dock. Which one are you trying? Maybe you also need the driver for that or the special "adapter/dongle" that they have.