I don't want to pop any bubbles, but I have to confirm that Windows 8.1 isn't broken. All the troubles I had with it, came from third party software and drivers it seems.
How did I manage to fix it.
Well, I went back to Windows 8 (the image I made just before upgrading to 8.1.)
From this point, I uninstalled all the programs I knew that had trouble with 8.1.
- Adobe Creative Cloud
- Adobe Dreamweaver CC
- Oracle VirtualBox
- iolo System Mechanic
- anti-virus software (my case AVG.)
And also some other programs that had accumulated during the year, especially if any toolbars had managed to get installed. I did this with Revo Uninstaller, because this program also deletes the stuff that stays behind in the Registry and maps on the hard disk.
And then, I did my upgrade again from the store.
SkyDrive worked just fine and my Apps as well. This problem was solved immediately.
After I was done checking, I managed to install the Adobe software again. There was an update for the Creative Cloud software, and I knew that Dreamweaver could be installed, it only couldn't be installed before the upgrade. I believe the other CC Adobe software causes the same problems as well. So, uninstalling before the upgrade is the best way to go.
I then tried my sleep function for a full day, before I added any other software. It worked for me, until the next day. In the morning, when I woke up the PC, it was suddenly stuck. My screen stayed black while the PC started but didn't do anything. Obviously a crash of something, but I couldn't find any information about it in the logs.
Then I deactivated Hyper sleep. Same result the next day. I then deactivated Hibernation, again same result the next day. Although, I did notice that the tasks the PC had to do in the morning, had been done. So, the PC only crashed after I invoked it to wake up.
This could have several causes, although, because it seemed that my PC did try to wake up but that my screen didn't receive the wake up call, I decided to look for new drivers for my Graphic card. It's an AMD Radeon HD 5800 Series, btw. I found the Catalyst Control Center version 13.9 and installed it on my PC.
And from that moment on, my PC slept and woke up without problems. I reactivated Hibernation yesterday, and this morning, the PC woke up again as when Windows 8 was on it.
The only thing I noticed, that is different from before, is that as long as my TV is on, which is connected with a HDMI cable to the PC, the PC stays awake as long as I'm watching it.

Now, for me, this isn't a bad thing, because I have also some stuff on the PC that I sometimes watch through the network connection with my Cable digicorder. In the past, I had to get up to start my PC if I wanted to watch something on it.

And, the good thing is, after I shutdown my TV and Cable box, it takes about 2 minutes for my PC to go to sleep.
For me, it seems Windows 8.1 wasn't the guilty one, but some of the other software that I had installed that I now have removed from my PC. Btw, Oracle's VisualBox 4.3.2 isn't buggy anymore. I presumed it was, because my PC didn't go to sleep after installing it, but I was watching TV while I waited it to go to sleep. At that point, I didn't knew this kept my PC awake.
The Toshiba laptop, I also reinstalled again by removing everything from my PC and to do a clean install. It has less software on it and doesn't take too long to reinstall.
On my Acer netbook, I could reverse the things iolo System Mechanic had done to it, and after I had done this and removed the software, it works now also as it should.
During the whole process, I made one little mistake. I did most of my troubleshooting on the Toshiba laptop, and when I had done a clean install, for some stupid reason, I had installed iolo System Mechanic on it without thinking.

If I hadn't done that, maybe I had found a solution much earlier. Slap to the head!
I hope that you guys can find a solution for your problems as well. At least, I can confirm now that Windows 8.1 can work as it should, if you can find the guilty party.