PC turns on normally once; then will not until the next day

[Ben.]

The PC in question:  Gateway FX6831, Windows 10, i7 processor 860, 16GB DDR3 RAM, 1.5 TB HDD, Blu-ray/Super-Multi combo drive, DVD-Super Multi drive, ATi Radeon HD 5850 1024MB video, Integrated LAN 10/100/1000, no modem, USB optical mouse, no web cam, BIOS P01-A2, Logitech stereo speakers, Manufactured: 2010.  Power cord is plugged into a Monster power control strip.  Power switch on PC works normally when PC is turned on about 6 a.m. each day.
 
HISTORY:  Worked normally until 04/20/2016, the day after I uninstalled Apple Quick Time 7.  A system restore to just before that did not fix the problem.  The PC turns on normally early in the morning (about 6 a.m.), however, is totally unresponsive after either Hibernate or Shutdown.  Next morning, it is normal again until after either Hibernate or Shutdown.

Since it turns on normally first time each day, which occurs early in the morning, I suspect some setting or instruction in Windows 10 is causing... and, controlling this?  But, I have not found anything suspect in the Power setting... and, have exceeded my knowledge level with regard to other settings/instructions.

[Geek-9pm]

Your PC is now about six or seven years old. Right? There are a number of things that can 'wear out' in time. 

First, try another video card. Next remove and swap out memopry sticks. If that does not help, the motherboard may have some component that has gone bad.

Most common are the electrolytic capacirtores. The is no esy way to test them other tahn intgrusive  testing.(Whaich menas yhou remove one and replace it with a new one.)
Do you have some test erqkuipment?

for what it is worth, here is a video albout testing motherboard cpaciltors.
https://www.youtube.com/watch?v=ngA4k32jLGc

Hope you find the problem. 

[Allan]

1) Don't use hibernation.
2) Does it reboot normally (as opposed to shutdown)?