Whenever I downloaded a new .dmg (in this example I will call it myprogram.dmg) file and tried to run it nothing happened. I tried rebooting, updating (to 12.4) and control+click -> choose DiskImageMounter but it refused to open.
To get around this I opened Terminal (either search for it or open via Finder -> Applications -> Utilities).
Change directory to where you downloaded dmg file. In my case It is in my download folder
The run the following command to mount the dmg file for installation
hdiutil attach myprogram.dmg
You can then install from there.