There were times when the District of Columbia delegation went off to the Democratic National Convention primed to lobby for greater home rule, confident that they would have a key role in a brokered convention and firmly under the leadership of the city's top elected officials.

But when the 19 delegates and their alternates take the floor in Madison Square Garden tomorrow night, there will be as many leaders as followers and only a token concern with lobbying on behalf of the foundering full congressional voting rights drive.

The delegates are all committed this time, either to President Carter or to Sen. Edward M. Kennedy. Most are for Kennedy -- and this convention is likely to be firmly run by Carter supporters.

Even the traditional black tricornered hats symbolizing the District's quest for full voting rights in Congress and its status as "the Last Colony" -- have become an option. This year, the delegates chose instead styrofoam boaters and plastic visors.

"I think it won't be as much fun this time," said Democratic National Committeeman John W. Hechinger, who attended both the 1972 and 1976 conventions and will be in New York this week.

Hechinger said there was some enthusiasm for the voting rights effort. But he added, "The main thing is the nomination of presidential and vice presidential candidates and that's finished. All the brokering and phone calls, all the speculation about who's switching or not, isn't going to be a part of it this year.It's all done."

The District's delegation is not only atypical in its 12-to-7 support for Kennedy at a convention where most favor Carter. But it is also a delegation dominated by elected officials. Many others are not.

The delegation includes a wider array of elected officials than ever before: On the Kennedy side, Del. Walter E. Fauntroy, along with City Council members John Ray, David A. Clarke, Nadine Winter and Betty Ann Kane: on the Carter side, Mayor Marion Barry, council chairman Arrington Dixon, council members Charlene Drew Jarvis and Wilhelmina J. Rolark, as well as school board vice president Barbara Lett Simmons.

Barry's on-again, off-again support of the "open" convention scenario has provided the only local suspense. Barry, considered by many a closet Kennedy supporter, said he favored defeat of the controversial proposed rule that would clinch the nomination for Carter by binding delegates on the first ballot instead of having an open convention. On Thursday, however, Barry reversed himself and said he would adhere to the official Carter position on the issue, which is to support the rule.

The six other Carter delegates, interviewed repeatedly in recent weeks, all say they are firmly in support of the rule. Most of them add, moreover, that they have not even been lobbied by Kennedy delegates and campaign workers to change their minds.

Local Kennedy campaign leaders privately say that they consider the D.C. Carter delegates a lost cause, and acknowledge that they have done little to try to shake them loose. They say they will begin their appeal after the group reaches New York, stressing Kennedy's stand on job-creating economic policies, but are not hopeful.

"Maybe we could do something if these [Carter] people were, say, labor leaders or somebody else," said one Kennedy delegate. "But they're elected officials. They've been around, they are harder to work on."

With Carter's forces in control of planning for the convention, the local Kennedy delegates -- though they dominate the delegation -- are forced to surrender some power to D.C. Carter supporters.

Delegation meetings, while chaired by delegation chairman John Ray, have often been dominated by Carter supporters better informed about preparations, like Democratic State Committee chairman Robert B. Washington Jr.

The distribution of floor passes and guest passes needed for access to Madison Square Garden, for example, is controlled by Carter's supporters. Efforts to increase the District's allotment of six guest passes have been channeled through Carter supporter Washington.

In sum, the delegation is expected to occupy a kind of backwater at the convention, far removed from the main action. That is an unusual role for District Democrats, who make up more than 70 percent of the registered voters in this city and whose intraparty politics have been considered the only ball game in town.

The true leadership of the delegation is unclear. Ray, a first-term councilman who was an obscure city politician only three years ago, is the titular head of the delegation, largely because he got in on the ground floor of the local Kennedy movement, with an early public endorsement while others were waffling.

In the hierarchy of city politics, Fauntroy, who also supports Kennedy, outranks Ray. But Fauntroy came on the Kennedy bandwagon later, and will have to assume a lower profile at this convention. In past years he has led the District delegation and, often to the anger of many, been its major powerbroker.

The real heavyweights of city politics -- Barry, City Council Chairman Arrington Dixon and D.C. Democratic Chairman Washington -- chose the wrong side in the May 6 presidential primary. They support Carter. And within their ranks, Dixon has consistently taken potshots at Barry.

The delegation has spent considerable time and energy deciding how to slice up the approximately $10,000 raised to help defray expenses. The first plan was to give the money to delegates according to individual need.

Lillian Huff, the ample, earthy and outspoken vice chairman of the delegation, was one of the prime backers of that idea. "I know I'm not going out to raise money for somebody like Mr. Hechinger," she told the delegates at one meeting. Hechinger is president of a string of home improvement stores in the Washington area.

But other delegates, including Barry, argued that a more equitable way would be to distribute the money equally. Those who didn't need it would return their shares to the pot. "That way, nobody has to be embarrassed," Barry said.

The equal-share view prevailed. The delegates voted to spend $4,000 of the money on group activities -- including a $200-a-day "hospitality suite" for parties and meetings at the Roosevelt Hotel, the delegation's home base. The remaining funds will be split equally.

After the decision was made, Hechinger left a personal check to the delegation kitty for $600. He also said he plans to turn down his share.