Here's some more (although a lot of this stuff spans more than the '80s):
Joy Division, New Order, Skinny Puppy, Dead Kennedys, DOA, Cabaret Voltaire, Anti Nowhere League, The Exploited, Tangerine Dream, The Residents, The Fixx, Style Council, The Replacements, Hoodoo Gurus, Big Country, The Stranglers, etc...
Nobody liked shredders? Racer X? White Lion? Jason Becker? Oh well. Some others on my list...
Van Halen (favorite ever)
Ozzy (only Randy stuff)
Yngwie Malmsteen's Rising force.