Screen saver + Energy Saver (Computer Sleep + Display Sleep) won't work since Mavericks

Question

Howdy,
Sorry to bother you.
My computer: iMac (21.5-inch Mid 2011), Mac OS X (10.7.3)
It took me some time to upgrade to Mavericks, but I did it eventually.
After having some problems with Spotlight (which was infinite looping indexing... and I just had to turn if off from Terminal), I realized I was encountering another big problem to me since the installation of Mavericks.
In System Preferences:
- 'Desktop and Screen Saver > Screen Saver' : it is set to 1 minute;
- 'Energy Saver > Computer Sleep' : it is set to 10 minutes;
- 'Energy Saver > Display Sleep' : it is set to 5 minutes;
- 'Energy Saver > Put hard disks to sleep when possible' : it is checked.
- 'Energy Saver > Wake for network access' : it was checked. I unchecked it. Nothing changes.
- 'Energy Saver > Start up automatically after a power failure' : it is unchecked.
- 'Energy Saver > Allow power button to put computer to sleep' : this option is absent from my System Preferences > Energy Saver, but I would like it.
So, before Mavericks, everything was working great.
Now, after 1 minute, or after 5 minutes, or after 10 minutes: it's all the same. Nothing is sleepy. Nothing is energy saving.
I did not change anything in my computer since I've updated to Mavericks. However, I changed Wi-Fi. Since it was the only new change, I've "played" with 'Energy Saver > Wake for network access'. When I opened my System Preferences, it was checked. I unchecked it. It did not change anything. I'm not sure what it's used for.
I would appreciate any advice to make it work as it used to.
Thanks for your time reading and typing your answer,
Have a good day,
Regards,

Answer 1

- 'Energy Saver > Allow power button to put computer to sleep' : this option is absent from my System Preferences > Energy Saver, but I would like it.
Built into the Software now.
Do a backup.
Quit the application.
Go to Finder and select your user/home folder. With that Finder window as the front window, either select Finder/View/Show View options or go command - J.  When the View options opens, check ’Show Library Folder’. That should make your user library folder visible in your user/home folder.  Select Preferences/com.apple.systempreferences.plist. Move the .plist to your desktop.
Restart, open the application and test. If it works okay, delete the plist from the desktop.
If the application is the same, return the .plist to where you got it from, overwriting the newer one.
Thanks to leonie for some information contained in this.
You might try Spotlight again. That is how the App Store knows what is installed.