My surface pro 3 has been with me for a few years and this problem has been with it for the same time.
If I leave the tablet shut down / sleep / hibernate, whatever I choose, for a few hours or longer, it won't wake up without a power cord attached. If you connect the power cord, it starts well.
Rarely it won't start even with a power cord, and then I figured out that the only thing required is unplug the power cord and plug it again, then the surface pro 3 can be started.
It does has a battery, if it wakes up, you can take away the power cord and use it on battery only.
The button combination never works.
Resetting the battery settings doesn't work.
Updating the software and firmware doesn't help.
Because of this issue, I can not use it for my daily work. Just use it as a leisure time tablet. Anyone has any clue? Thanks.