I feel your frustration. Would you mind trying one test to determine if the PC will wake up to run tasks other than the backup.
Create a scheduled task of your own to wake the PC at a specified time (let's say 15 minutes from current time. In the Action tab have it run a program - try notepad.exe. Leave options in the settings tab at default.
Save the task and let the PC go to sleep (set it for 10 minutes).
PC should wake up approximately 5 minutes after going to sleep
If you have left the laptop lid open then when the PC wakes up this display should stay black but you should be able to tell from light activity whether it wakes up or not. If you think it woke up then activate the display using the keyboard (you may be prompted to login based on your account settings). When you get to the desktop do you see the notepad window open?
Mike