Settings made via OS 9's control panels are retained in preference files. One or more of the applicable preferences files may have become locked, or damaged.
Go to System Folder > Preferences. Locate the file named Display Preferences and the file named Monitor Preferences (the second one may be in a folder having the same name). Neither should be locked. If either is, you can unlock it ny doing a Get Info (Command-I) on the file.
If neither file is locked, try throwing both of those files away, empty the Trash, then restart. New prefs files with default settings will be created automatically. This means you may need to redo the resolution choice as well as other settings, but you should need to do that only once.
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Another possibility, perhaps additional....
If that machine had been stored for a long while, the internal battery may be too weak or dead. If that is the case, replacing it is the solution.
However, if that machine is a Beige/Platinum desktop model (not an iMac nor a B&W), chances are the battery is okay - those older desktop G3 models usually won't display anything on the monitor if the internal battery is shot.