In this case I don't believe that WOL is going to be the culprit - the system is never entering a low power state to begin with, so the interference is from the OS side of things, not the BIOS hardware side.
However, WOL may still restrict the system's ability to enter and *stay* in a low power state if this other issue is resolved, so keep that in mind as well, Ivan.
*Also* your network card(s0 configuration page may *also* contain information regarding WOL - this can be controlled in the OS as well, not just in the BIOS anymore, at least for some NICs - on my Advanced tab at the bottom of that long list o items, There are 3 settings for Wake on - Magic Packet, pattern match, and WOL from PowerOff.... Again, those may be of interest to you later on if you machine continually wakes up once you get it to start entering sleep mode....Therefore my original statement in this post may be completely wrong and WOL *may* be the culprit after all - I didn't know until I went exploring that the OS can handle WOL / Magic packet monitoring.
I know that you tried disabling the setting "Allow this device to wake the computer" but did you try disabling the *top* setting - Allow the computer to turn off this device to save power?
Finally, since this is a wireless adapter, and the computer *does* go to sleep when you use wired, what software (other than the driver) did you install when getting the wireless NIC working?