Clicking the Show Desktop button does not work, but the keyboard shortcut works fine.

Because Win+D still minimizes all windows, the desktop shell itself is responding; the problem is probably limited to the taskbar corner setting, Explorer, or the current user profile. First open Settings, go to Personalization, Taskbar, Taskbar behaviors, and enable the option that lets the far corner of the taskbar show the desktop. If it is already enabled, turn it off, restart Explorer from Task Manager, and enable it again. Next install pending Windows updates and restart. If the corner still does nothing, run DISM RestoreHealth followed by System File Checker from an elevated terminal. A clean boot can identify a shell extension or utility intercepting the click. Finally, test with a new local user profile. If it works there, the issue is profile-specific rather than a system-wide Windows defect. Keep Win+D as a safe workaround while isolating the cause.