Why won't my mac screenshot

Please tell us which Mac, model and year you’re having trouble with, and what macOS version you’re running. Find that info by clicking the Apple menu () at the top-left of your screen and then select About This Mac.

(Note- for privacy and security please never post your serial number.)

Meanwhile, see if the problem still happens in Safe mode (press and hold the shift key down at startup). It can take much longer to safe boot (5 min) so be patient.

How to use safe mode on your Mac - Apple Support 

Safe mode very often corrects weird software behavior by forcing the OS to do cache clearing and other housekeeping. When you're in safe boot, the machine will not be at its best performance, especially with graphics, but that's expected.

Does the problem persist while in Safe mode?

Often not required, but consider allowing the Mac to "soak" in Safe mode for an hour to allow maintenance routines and processes time to complete, then exit safe mode by restarting your Mac normally and re-evaluate the issue again.

Two suggestions:

If the default key chord is not working try resetting keyboard shortcuts to defaults:

 (Apple menu) > System Preferences (or Settings) > Keyboard > Shortcuts > Screen Shots > Restore Defaults

If you are using the Dropbox product, it can intercept screenshots so they won't appear on the Desktop.