Password Protected DMG File is not opening

So you are running Disk Drill on the contents of the encrypted .dmg file? If so, then it means that it is being unlocked. You can try running Disk Utility First Aid on the unlocked contents of the .dmg. I don't know if it will appear in the sidebar or not since it has not been mounted yet. If the .dmg is being unlocked, then perhaps it is possible to manually mount the contents in read-only mode by using the command line so you can access the data. Before doing anything with this .dmg file you should make a copy and work from the copy in order to keep the original file untouched from this point so no damage (or further damage) occurs to it.

There is a free open source app available you could try, but I don't know if it is compatible with Monterey or APFS volumes. PhotoRec and TestDisk are two apps from the same developer which can be used. I've personally used TestDisk several times (it is a command line utility).

If you don't have a backup and these apps don't work, then you don't have much choice but to pay up for the app to attempt to recover the data or by contacting a professional data recovery service.

Can you still open the .dmg file remotely using the other computer?

macOS Monterey has changed its behavior with some encrypted drives especially if they use the HFS+ file system. Or whatever caused your computer to freeze may be responsible for the problem.

Try restoring from a backup to see if the backup copy of the .dmg before the last modifications were made will open.

You should always have frequent and regular backups of your computer and all external media (including the cloud) which contains important & unique data.

Monterey apparently has problems when it comes to opening password protected DMGs. I’ve had trouble both using HFS+ and APFS. Works for a while, then stops working. I put in the password, click enter, and… just nothing. No error message or anything. It’s freaking me out so much that I am putting files, when I can access them, on unencrypted thumb drives, and storing them in a safe. I should not have to do that. Never had any problem with DMGs for years and years.