When you power on the computer from being totally off, hit one of these keys:
F1, F2, or delete
This will let you enter CMOS (some basic options), where you may be able to change some power options. If you can, get to where the "POWER" options are and see if "Wake on LAN from S5" is Enabled...If it is enabled, highlight it, press enter and change the setting to "disable".
If there is another setting, "wake system from S5", highlight it, press enter and change the setting to "disable"....Once you are done, be sure to save your changes by hitting the F10 key, or going to the EXIT options..
If the problem goes away after adjusting these settings, then problem fixed!