I created an account to add to the solution offered here for any future bug-solution-seekers. Deleting the whole /AppData/Roaming/StardewValley folder does in fact work, but it has the downside of also deleting your save files. Those can be restored from Steam via cloud save (if enabled) but you don't have to nuke the whole folder.
Inside the /StardewValley/ folder is a small 7kb extensionless config file "startup_preferences" -- if you delete that file and launch the game the problem (startup music, startup scroll, but no accessible menu where you just get stuck looking at the clouds) goes away immediately with no requirement to delete your save files. Hope that helps somebody in the future! Thanks to posting your solution Toasted, because it led me to the more compact version of just nuking the preferences config file.