I have a Gigabyte MA785GT-UD3H mainboard. I want to wake my computer up using Logmein, however, I could not found any WOL option on BIOS.
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...
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.