Trouble getting VLC installed properly and working

[stevef]

An effective backup policy is highly recommended.

I think I want to remove and reinstall VLC. Maybe the problem can be fixed in place.

As you've already tried one method to remove and reinstall further attempts to do the same thing are unlikely to make things much better.
To try to fix what you have, we need to understand exactly what the current state is.
Does VLC run at all ?

What do you suggest that I do next?

In your position, I'd be tempted to re-install the OS.