I've always heard/read that it was the Sunset Tower building at Sunset & Vine.
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LAPL/Calisphere
The caption for this says:
Architect's drawing of Sunset Vine Tower, located at 6290 Sunset Blvd. in Hollywood. The 1963 18-story International Style tower, designed by architect Douglas Honnold of the firm Honnold & Rex, was the first skyscraper built in Los Angeles after the city repealed its 14-story building height limit.
Under construction: April 19, 1962. NBC Radio City in background. And a nice street lamp!
LAPL
A nice L.A. Times article
HERE, when the building was re-opening as luxury apartments, talks about the building's troubles, beginning in 2001 when "an electrical transformer exploded, plunging it into darkness and sending employees of 40 companies with offices there running down stairwells to safety. Because the electrical meltdown knocked out the building's fire alarm system, city inspectors and fire officials for months barred workers from entering to remove files, office equipment and personal property. But with the building's tenants locked out, vandals moved in, trashing some offices and stealing files and equipment. Neighbors were soon calling the place 'the world's biggest crack house.' Authorities ordered the tower fenced off about six months after the explosion."
Workers dismantling rooftop equipment with a cutting torch accidentally set the tower on fire in 2005.
Because the elevators were still out of service, firefighters had to carry hundred-pound loads of hose and gear up stairwells to fight the flames. Later, they had to undergo decontamination because of asbestos exposure.
Currently:
ArchDaily
P.S.: This building was shaken apart in the 1974 film Earthquake.
Matte Shot