Has anyone ever had shift command 3 or shift command 4 work for taking a screen shot? And, what is an answer that works for taking a screenshot?

Well, I have been using Command-Shift-3 and -4 for more than three decades. Yes, it goes back to the old "classic" Mac OS from last century. It has never failed.

I wonder what may be wrong with your system.

Go to System Preferences->Keyboard->Shortcuts->Screenshots.

What do you see? Are the boxes checked? Do you see some different keyboard shortcuts? What?

First, launch the Screenshots app from the Applications folder, click on Settings and set the location to save the screenshots to the Desktop. Now try those key combinations again.

If they still do not work boot into Safe Mode according to How to use safe mode on your Mac and try those keystrokes for screenshots. If they work reboot normally and try again.

If they don't work after a normal reboot it means there are some 3rd party software that is interfering with them. Post back with the results and we'll go from there.

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

Make sure you are pressing the combinations correctly. If you have trouble doing combinations on the keyboard...enable sticky keys(that's what I do since I usually have trouble). You can access it by going to system preferences -> accessibility -> then keyboard -> and press on enable sticky keys(make sure the check mark is there next to it). It should say sticky keys on. You can always disable sticky keys anytime you like.

I use it all the time, and have for many years. It sounds like you have third party software installed that's grabbed those keystrokes for themselves.

It works for me. Have you tried going to the screenshot app(In a mac by default)? That is how I take screenshots.

Have you also tried shift command 5?

Good work :-)

Listen to @welcome160 and use the default 3 key combination suggested.