Product specifications at Realtek state that the 8111c supports WOL.
This extensive Thread at Logmein details what steps you need to follow to enable WOL via Logmein. From the main post that details this...
Please confirm that the host is in a supported sleep mode (stand-by, sleep, or hibernation mode: ACPI specification S3 or S4). For a Windows PC that is powered off (but still plugged in), confirm that Wake on LAN is enabled in the computer's BIOS.
Tip: Consult the user guide of your computer or motherboard to locate the appropriate BIOS switch, (usually Wake on LAN from S5).
Please also confirm that at least one other LogMeIn host on the same LAN is online and available.
Now... your motherboard manual indicates on page 53, that if EuP is ENABLED that wake on LAN becomes unavailable. Since there appears to be no direct control to enable and disable it, if you have the proper ACPI power state enabled, WOL should work as long as you leave EuP disabled.
As the thread at Logmein support get to detailing... you need to make sure you have port 9 forwarded to that computer's internal IP address in your router. In fact, just read that thread as a good once-over.