Screenshot paste only works in some apps, not in Google Chrome
Solution 1:
I've seen this kind of behaviour with other functionality, try the following command in Terminal (may require sudo)
Change directory to "/System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/LaunchServices.framework/Versions/A/Support/"
cd /System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/LaunchServices.framework/Versions/A/Support/
./lsregister -kill -seed
OR
/System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/LaunchServices.framework/Versions/A/Support/lsregister -kill -seed
This rebuilds the launch services database, sometimes corruption in this can cause weird behaviour
EDIT: Since the above didn't help let's try something else. When you use shift+control+command+4 to copy a section of the screen to the clipboard you can view the clipboard contents. To do so, switch to Finder and click Edit > Show Clipboard to show the contents of the clipboard. You should see something like this window pop up that says "Clipboard" at the top and has a description of the clipboard contents in the bottom-left corner. Do you get the same thing?