Power button no longer wakes computer from sleep

My current Win 7 installation was installed in July, 2013. From the time I installed it, I would put it into sleep mode by going to Start > Shut Down "arrow", and selecting Sleep every night. It would go to sleep and the power LED would flash. I would then press the power button the next day and it would wake up.

This worked perfectly until the last week or so. Now when I press the power button the power LED continues to flash for about 3 seconds, and then the light goes out. The only way I can get it to turn on is to press the power switch on the power supply to the off position, leave it off for a few seconds, flip it back to the on position, and then press the power button on the front.

When the computer comes back from this state, it acts like it's turning on from being fully turned off (I see the BIOS screen, etc.), but all the stuff I had open are still there. I guess this is like coming back from hibernation?

I don't know what happened to cause this. I have made no changes to the power configuration, no hardware changes, no driver updates. Maybe it was a Windows update that caused it?

How can I make the power button wake up the computer like it used to?

Thanks!

I can think of 3 reasons
1. The wiring for the switch could have detached from the motherboard (doubt that).
2. Maybe windows is having issues resuming from sleep (I also doubt that).
3. Hibernate is turned on.

Disable Hibernate and see if it works Hibernate - Enable or Disable

Also, you can enable the keyboard to wake the computer through device manager.

Look at Windows Update History to see what Windows updates were installed since the problem started.
Look at Event Viewer for any Errors and Warnings that could help determine what the problem is.

Do you have a Restore Point, or better yet a System Image backup from before the problem started ?
If you do, you can try Restoring from before the problem started.
If you have Restore Points, you can view changes that Restore Point would "undo".

If "restoring" works, start re-installing updates and changes one at a time to try and find what update/change caused the problem.

But the OP stated

When the computer comes back from this state, it acts like it's turning on from being fully turned off (I see the BIOS screen, etc.), but all the stuff I had open are still there. I guess this is like coming back from hibernation?

To me that sounds like it is resuming from Hibernate, not the same as cold boot, the previous session is "resumed".
I see this when i sleep a PC using Hybrid Sleep, and power is interrupted while sleeping.
If I turn off power when in hybrid sleep, the PC resumes from hibernate, as it should.

imho, the question is to why the OP PC "flips" to hibernate, shortly after entering sleep, if power is not interrupted.

Also, for me a blinking PB light indicates I'm in S1 sleep state.
I use S3 sleep, the PB button does not blink, it's a deeper sleep state than S1.
I don't know if this is important, i only use S3.

Sleep States - See Available Sleep States