Hello davidhmorgan and welcome to Apple Support Communities.
It appears you are having an issue involving QuickTime Player and screen recordings
First, make sure you are using QuickTime Player and not an older version that might still be on the Mac from an older macOS installation.
Next, there are a couple of steps you can take to help isolate what is causing this.
1) Start by doing a safe boot of the Mac. This will clear some cache files, turn off some system extensions and log-in items and give you a good foundation. After doing the safe boot, reboot normally and test.
How to use safe mode on your Mac
2) If the issue persists after a safe boot, set up a test user account in order to isolate the issue to the system or the user data and ultimately resolve it.
How to test an issue in another user account on your Mac - Apple Support
Cheers.