Because the programmers were lazy, RPGMaker is very particular about where it lives. Do not put the game folder:
1. On an external drive
2. In a deep directory structure (folder in folder in folder)
3. Anywhere on the system drive (the drive Windows is installed on. So if you downloaded to "downloads" or "documents", move it.
4. Anywhere with potentially weird read/write permissions.
5. Within any directories with really long names (I'm not talking the old dos restriction of 8 characters, I mean like 24+characters. And yes, the game's own folder name is long, but ONE usually isn't enough to do it. It's multiple combined in the path that tend to break things).
For the sake of testing:
1. Download a fresh copy of the game.
2. Unzip it and place the folder on non-system drive, not in any other folder. If you only have the one drive (fairly rare these days), you'll have to manually check the write permissions on the folder.
3. Copy the contents of the "save" folder from the old install to the new one. This should carry over your saves. You can copy the datacrystal file as well if you like, though this isn't needed for testing.
4. Play from the closest save and get the lucky rabbit bad end again. It should work properly, verifying that this location quirk was the issue.
If you'd rather not bother with all that and aren't interested in diagnosing the bug, just fixing it quickly: Normally in the game's www\img\titles1 folder there are two title backgrounds, TitleBG.png and Alt.png. Getting the lucky rabbit bad end name-swaps them, but if the game doesn't have proper permissions or gets confused somehow, this fails. If you still have an Alt.png, rename it to TitleBG.png. If not, you can get both files from a fresh version of the game. Title whichever you would like to be the bg TitleBG.png, and the other Alt.png.