Jim Morrison was neither a musician or a singer before the band got started, he was an artist interested mostly in poetry and philosophy but also in directing and producing films which is what he pursued his degree in at U.C.L.A. His father, who was a famous Admiral in the Navy, hated that Jim was wasting his time on the arts so their relationship was terrible.
A friend of Jim's from UCLA who was a musician, and later bandmate, read one of his poems and thought it would make for a great song. He asked Jim if he could sing and he said he couldn't but he got Jim to sing anyway and he was mesmerized; he wanted to form a band immediately. Jim came up with the name: "The Doors," because of a philosophy book he read that covered the fact that if the doors of our lives were cleansed before we walked through them, that we'd see the truth on the other side instead of our perceptions.
The band skyrocketed to fame even having at one point the great band: "The Who," open for them. But what a lot of people don't know is that their first official large city tour in the U.S. crashed and burned as Jim Morrison got drunk before the concert (he had developed a major alcohol and drug problem), and was caught by a police officer having sex in the bathroom, he used profane language during the concert, he exposed himself to the audience, and made other gestures of a sexual nature, so the police pulled him off stage. He was arrested for one felony (showing his genitals to the crowd), and a few misdemeanors.
Jim was subsequently found guilty and was sentenced to serve four months of hard labor in a Miami prison. While waiting to find out when he'd have to serve his time, he travelled to Paris and began working on what would be his fourth book of poetry. He told his long-time girlfriend that he wasn't feeling well and was going to take a bath. She later found him in the tub and it was pronounced that he had died of a heart attack; all those years of drugs and alcohol had finally done him in.
One of his songs that went to number one was called: "Come On Baby Light My Fire." The thing about someone burning out is that you must be on fire in the first place. Jim Morrison was on fire if only for a brief period of time as he died in 1971, at the age of 27.