The problem is that when it's asleep a key press won't wake it up. Only pushing the power button or using wake-on-lan will.
One thing I just thought to try is using an app on my phone to send the WOL packet.
One thing I just thought to try is using an app on my phone to send the WOL packet.
Edit - the other thing that came to mind was to look into HDMI cec and see if there's a setup where turning on your tv will turn on the PC automatically.
Edit 2 - if you go with an app, you could use something like tasker and then you can have different triggers like your phone tapping an nfc sticker (then you don't have to unlock and find an app).