If you downloaded the “Ethernet Driver” from Sony’s support page and you noticed that is not good at all, here is how I made it working.
Searching for the PCI ID found in Device driver list has ended in no useful stuff, only spam results.
Going back to the source of this driver at http://www.sony.ro/support/ro/product/VPCEH3S6E_W/downloads/REDETH_00247766_0042_5704 I have seen the version of the Realtek driver:
Realtek PCIe GBE Family Controller, Version 126.96.36.1991 for Microsoft® Windows® 7
Searching for this sentence, I have found the HP page: http://h10025.www1.hp.com/ewfrf/wc/softwareDownloadIndex?cc=us&lc=en&dlc=en&softwareitem=ob-94199-1
On this page is the exact version that we need:
Microsoft Windows 7 (64-bit)