As a child, Jesse Jackson watched his half brother play with a new bat and baseball in the big back yard of the home of his middle-class father, a man who acknowledged the young Jackson's parentage but never brought him into his home.

Jackson, the illegitimate son of a teenage mother, grew up on the outside looking in - outside of mainstream South Carolina life because of his race, outside of his own people because of his birth.Jackson didn't let it beat him down. Instead, the pain drove him to seek legitimacy, to gain the respect denied him as a child.

Tuesday night, in his acceptance before the Democratic National Convention, he got that respect.

And in so doing, the man known for his rising, inspirational speeches didn't disappoint anyone in the Omni.

"I know what it's like when no one knows your name," he told the thousands who cheered him. "I wasn't supposed to make it. Like some of you watching tonight in the projects, on the street corners, I know abandonment. I know what it's like to be told you're nobody and won't be anybody.

"But when my name goes into nomination for president of the United States Wednesday night, your name goes in. Hold your head up. Stick your chest out. In the morning the sun does rise.Hold on. Hold on. Keep hope alive. Yes. Keep hope alive!"

The delegates loved it and broke into applause dozens of times. Some in the audience shouted back at Jackson, giving the packed Omni the flavor of a religious revival.

Knowing that he has no real chance to win the nomination Wednesday - Dukakis has more than enough delegates to win on the first ballot - Jackson warned he won't disappear.

"Jesse Jackson is tired of sailing his fragile, small boat in the safe harbor. I'm going into the deep water, with the big boats." He said he'd rather go down in a good fight than remain in a safe portage.

He struck, again, many of the themes of his campaign - better health care for the poor, adequate day care for children, compassion for the sick and disadvantaged, equal rights for women and minorities and an all-out war on drugs.

Jackson said Dukakis promised common ground on many issues and that Jackson would play a significant roll in the nominee's fall campaign. But Jackson also warned, in a mild way, that those promises must be kept.

Still, he clearly accepts Dukakis as the nominee and seeks accommodation with him. "His (forefathers) came on immigrant ships. Mine came on slave ships. But we're all in the same boat now."

The screaming and yelling of the delegates, the national television audience, the winning of most of his planks in the party platform, the agreement that he will name a number of members to key positions in the National Democratic Party - all could have been only dreams just two years ago.

Now it is real. And Jackson clearly wanted all those left out of what he called Reagan's exclusive club to share in his accomplishments.

Jackson was preceded at the podium by John Kennedy Jr., son of former President John Kennedy, who introduced his uncle, Sen. Edward Kennedy, D-Mass. - a man if not for his ruinous Chappaquiddick car accident, may have been a Democratic presidential nominee himself.

The senator used some of the toughest language so far in condeming Vice President George Bush, who will win the GOP nomination next month in New Orleans.

Kennedy recited a litany of foul-ups in the Reagan administration, asking at the end of each: "Where was George?" when things went wrong. The delegates soon got the drift and shouted "Where was George" along with him.

Kennedy ended his speech with an emotional remembrance of his brother, former Sen. Robert Kennedy, and Atlantan Martin Luther King Jr., both assassinated in 1968.

"We (Democrats) are the trustees of a dream. Twenty years ago we lost two of the most powerful voices of that dream. We remember them now to remind ourselves that the American journey is unfinished.

"Now is the time (to fulfill the dream)." Repeating the eulogy he gave at his brother's funeral 20 years ago last month, Kennedy said if King and his brother were here today, they'd say: "Some men see things as they are and say, Why? We dream things that never were and say, Why not? Now is the time."