Residents of two of Northern Virginia's oldest black neighborhoods yesterday succeeded in blocking a giant radio receiving disc from their community, but lost a fight to kill a planned doctors' office building there.

The Arlington County Board unanimously rejected a proposal from WETA-TV for the 15-foot-wide satellite receiving facility after members of Hall's Hill and Langston citizens associations complained that the public television station has been arrogant and insensitive to them.

By a four-to-one margin, the board approved a rezoning request needed for construction of the office building. It would be located adjacent to Hall's Hill, the oldest black enclave in the Virginia suburbs, established shortly after the Civil War by Freed slaves.

The county board, however, withheld specific approval of the design of the building, saying it wanted developers to offer other designs for the controversial five-story structure. The building would serve about 50 doctors and would be located next to the Arlington Hospital's grounds.

"This is an invasion in our community," said the Rev. Carl Renick, pastor of the Calloway United Methodist Church and a Hall's Hill community leader. "We have people living in the Hall's Hill area that have been here for years. They want to try and preserve their heritage and this will bring devastation to our community."

Lessie R. Hicks, president of the Langston Citizens Association in another predominantly-black neighborhood which borders the hospital, agreed. "The residents have roots here," Hicks told the board "(The developers) are asking this country board for a blank check so they can cash in on this community."

But hospital officials and more than 15 doctors told the board that the $3.5 million building, to be owned by the physicians, is needed to hold down spiralling health care costs and improve medical care for their patients.

Board Chairman Dorothy T. Grotos, the only board member to oppose the rezoning, disagreed. "Certainly it's very convenient to have doctor's offces next to a hosptal, but do we want to violate a residential neighborhood and put an office building there?" Board members then voted to defer final action on the design until September.

WETA executives conceded that they had community relations probleems in the past, but said they were anxious to improve the situation. They urged the board to grant permission for the disc which would receive and re-broadcast live concerts from other public broadcasting stations around the country.

"If we were talking about a baseball game or the Redskins, then maybe I'd say 'yes, approve it,'" Robert H. McGregor of Hall's Hill told the board. "But they're going to give us these symphonic sounds."

Other residents complained of poor commercial television reception because of an existing WETA-TV broadcast tower located on 19th Street. "While WETA claims that it is interested in enhancing the cultral life of the metropolitan area," Lessie R. Hicks complained, "it has been a poor neighbor."

In other action, the board approved a modified proposal by a Boston-based real estate trust to build a high-rise hotel and 13-story office complex at 2765 Jefferson Davis Highway near Crystal City.

In May, the board had rejected a plan by the North American Mortgage Investors fr the 18-story hotel and a 15-story office building there. The board then siad that although the developer had requested approval for several stories above the county's height limit, it had not offered to provide sufficient public improvements in return for the variance.

Several weeks later the firm filed a $6.5 million damage suit aginst the board, charging that the denial amounted to "legislative blackmail" because Arlington officials had approved even taller buildings in the same area. The firm's attorney said yesterday that his client would drop the lawsuit because the board had approved a substitute approval.