I assume you're talking about ethernet over HDMI, here's a quote from a page selling hdmi with ethernet cables:
"HDMI Ethernet Channel - The HDMI Ethernet Channel provides 100 Mbps, full-duplex Ethernet traffic along the HDMI cable, allowing a wired or wireless Ethernet connection on one device to be propagated to other devices. Note that for this feature to be functional, all pieces of equipment between the Ethernet source and the destination must support the HDMI Ethernet Channel feature."
The problem with your setup is that both the hdmi ports in question (the pc and the laptop) are designed to be outputs not inputs. So while I think it is possible for it to work, it's something the manufacturer's never even thought of implementing.