You don't need to touch your saves files. But, if you want to know where they are saved, check this info.
As for the game files are located where you download them. Just try do delete that folder and make the download again from this page.
You can even just download the game again from this page and try to start it from the freshly downloaded folder that shouldn't have any corrupted files.
I’m not sure if that will work. But that’s a functionality handled by the game engine, that’s why I think something in the files must have gotten broken somehow. Especially because it worked well previously for you, and now you can’t even start a new game.
PS: Another issue could be the “rollback side” option. Go to the options screen and check if you have that turned on. When it’s on, if you click at the very right, or left side of the screen (depending on which side is selected), the game will rollback. But not if you click at the center of the screen or use the space bar. I don’t think this is the issue, but you can quickly check that.