It's possible (but unlikely in real-world practice) that the database is protected only by a key file. KeePass v2 also allows a Windows account option. If this is the case, it would be trivial to break into the database just by finding the key file.
Luckily for you, KeePass itself remembers not only the last-used database, but also its file location, the file location of any key file, and whether or not a password was used to open it. For example, in KeePass2, you might see this in the user's config file:
I'm not sure exactly where or how KeePass v1 stores this information, but it should be similar. Check the file locations here: https://keepass.info/help/base/configuration.html