Try the solution suggested in this post
Re: Screensaver "start time" option grayed out
Back up all data. Quit System Preferences if it's running.
Triple-click anywhere in the line below on this page to select it, then copy the text to the Clipboard (command-C):
In the Finder, select
Go ▹ Go to Folder...
from the menu bar. Paste into the box that opens (command-V), then press return. A folder should open. If it does, look for a file with a long name that begins "com.apple.screensaver". There may be two such files. Move the one without the word "slideshow" in the name to the Trash.
Test. If the problem is resolved. recreate your settings in the Screen Saver tab.
My experience - On top of it I had to quit "System Preference" and open it again, only then it started to work.