But here's a question. Were any of those groups able to get people elected to national office, or anything but denounced by mainstream politicians/media?

Exactly, DJ.

there was a bombing right before LiveAid.

They were the bombees, not the bombers.

I don't think that they aimed to get people elected, did they?

Yeah, I think that's the thing. Of COURSE there are violent crazies on the fringe of any political position. ("Crazies" not to indicate actual mental illness, here.) But they are not generally taken seriously by the mainstream.

I just refreshed my memory of MOVE. They were basically a massive neighborhood nuisance, had killed one cop when their place was raided, got into another standoff when city cops tried to evict them, and then the city dropped a bomb that started a fire destroying 200 homes. So, violent? Somewhat. Nationally powerful? Don't think so.

And taken seriously by the mainstream=becoming part of the culture/society that we all participate and live in.

Yes, and I'm sure some of the animal rights fringe that blew up/rescued lab animals counts as lefty fringe...but again, one part of the party being so fractured is that wasn't exactly a huge platform and endorsed.

Gud, I have a hard time understanding how using gun metaphors in politics is not automatically violent rhetoric.

From an article in 2009 discussing the Tea Party and calls for armed insurrection. (This is following a section on a Tea Party anti-healthcare rally that had signs reading "Bury Healthcare with Kennedy.")

Where Can This Ugliness Lead?

The mean scene recalled another Kennedy. When JFK traveled to Dallas in November of 1963, the atmosphere was just as charged. "In that third year of the Kennedy presidency," William Manchester wrote in Death of A President, "a kind of fever lay over Dallas country. Mad things happened. Huge billboards screamed, 'Impeach Earl Warren.' Jewish stores were smeared with crude swastikas...Radical Right polemics were distributed in public schools; Kennedy's name was booed in classrooms; corporate junior executives were required to attend radical seminars."²

A retired major general ran the American flag upside down, deriding it as "the Democrat flag." A wanted poster with JFK's face on it was circulated, announcing "this man is Wanted" for--among other things--"turning the sovereignty of the US over to the Communist controlled United Nations" and appointing "anti-Christians...aliens and known Communists" to federal offices. And a full page advertisement had appeared the day of the assassination in The Dallas Morning News accusing Kennedy of making a secret deal with the Communist Party; when it was shown to the president, he was appalled. He turned to Jackie, who was visibly upset, and said, "Oh, you know, we're heading into nut country today."

Sounds pretty familiar... (Seriously, those editorials/letters to the editor from the DMN are nearly identical to the ones about Obama/Democrats today)