Yes, G is for magic packet and must be set. These pins are sometimes required for external (ex. PCI) network cards. Onboard does not need this, it is internally connected.
These computers are connected by switch or by router? Check if this entry in /etc/network/interfaces will help:
iface eth0 inet dhcp
post-down /sbin/ethtool -s eth0 wol g
Of course eth0, dhcp is only example, use your own settings. But I don't known if this is even interpreted when "Network Manager" package is used. I have uninstalled it as found it is needless.
Also please answer which client tool are you using to wake. I am using "wakeonlan" from Ubuntu repository. And one more thing, if you have nVidia network card, there was an error in drivers which causes a reversing of MAC address (and in my system assigning a random one), you can check your MAC if is correct on MAC lookup