I am also of the opinion that you did not train for the invisible fence and now your dog has no clear Idea of why he is being shocked, only that it happens when he has the collar on and when in the yard. To me it's pretty clear the E-collar has to go.
You can never go wrong with a fence.
To me, it is clear that the fence/collar needs to be re-trained from the beginning (or, from before the beginning, actually). There is no need for the collar to go.
Don't know about the whole universe, but where I live more and more homeowners' associations are prohibiting physical fences... sometimes, that simply is not an option.