The first thing I always do in this type of situation is back up my game saves so you don't lose anything during troubleshooting. Your saves are here:
C: \Users\[USERNAME]\AppData\Roaming\StardewValley\Saves
Copy that Saves folder and paste it into another location, like your Desktop or Documents. That way you always have that backup of your games. It's tiny, my 9 saves total 42MB.
Actually, could you make a test user on your machine and see if SDV works for that user. That will ID if your problem is specific to your userspace, or the machine in general. The following stuff should only come after doing that.
However I'm not sure what to do next as you've already done much of what I'd do. Have a look in the System Logs to see if there's something identifiable that happens when you load SDV and then it quits out. I sometimes find interesting things in there, there could even be a missing driver for your video card? Find the current version of that driver and install it.
Next I'd probably uninstall SDV,open the Registry, search for Stardew, and clear all the Stardew Reg Keys you find. There shouldn't be much as you've uninstalled it but frequently there are things left behind. But mucking about in the Registry can be dangerous, you don't want to delete anything not SDV-specific. I'll have a peek at my Registry and see what I find, though I play the GOG version of SDV.
Edit: I looked thru my Registry and of course SDV is littered through it, as mine is still installed. Still most of those could be removed if you find them after an uninstall. I see the XNA-related info you referred to as well as all the versions of SDV I installed. One thing I'd probably not change would be the SDV Port openings in the Firewall as I find those to be annoying to set up again for local multiplayer. Not a concern if you don't MP with other people in your home. Still, I see this Registry diving as a very last resort. You really never should have to mess about in the Registry.
