QGIS polygonize issue: GDAL DLL load failed

Could also be related to the fact that there are two QGIS executables that get installed, one without a lot of the additional extensions, one with. Check your shortcuts folder, there should be two icons/executables. Make sure you run 'QGIS Desktop with Grass 7.x'.exe

I've had the same problem. It's probably related to your GDAL version. With QGIS 3.10, some algorithms require GDAL 3.1, which is a higher version of GDAL than is currently distributed with QGIS. To confirm this in QGIS, go to View > Panels > Log Messages. If the GDAL version is the problem, you will see a message similar to this: "The 'GDAL==3.0.1' distribution was not found and is required by the application."

As a possible work around, if you copy the console line call from 'gdal_polygonize' to the end, you can paste and run it in the console to get the desired output with your current GDAL version.