It wasn't bad enough that they stole the clothes washer and dryer out of Cary Conn's basement at 919 I St. NW, or even that most of his socks were in the dryer.

It wasn't bad enough that they ripped off his TV, his bicycle, a clock, a radio and a pair of shoes on Nov. 23 while he was at work at the National Archives. The next day they broke in and stole two suits and $130, taking the loot away in his car, which they also stole.

It wasn't bad enough that he had to chase away a fourth burglar himself.

Now Conn's assailants -- who seem to be legion -- are getting ready to remove his house.

And that's what upsets Conn, a quiet sort of man of 38 who rarely gets upset about anything.

"It was just the house I wanted," he said with some despair. "It has 14 rooms, it has marble fireplaces, it's within walking distance of my jobs and I could afford it. I doubt that I will ever again own a century-old house as lovely as this one."

It makes no difference that this time the prepetrator is the city. Conn looks upon it as just another breaking and entering.

"I sit here and think if only they hadn't taken the house," he said. "But there's no hope left."

Both Conn and the D.C. police who say Conn may have set some sort of world's record for the number of burglaries in a week -- acknowledge his situation is unusual.

He bought the house in the fall of 1977 believing that the District's $99 million convention center, which is scheduled to replace it by 1982, "essentially a dead issue."

He took the three-story Victorian row house, which had been a rooming house since 1910, found new homes for a variety of tenants (including an elderly woman with nine cats), and set about pouring $17,000 into the building for renovations ranging from 50-cent plaster patches to a $1,200 new roof with a seven-year guarantee.

He installed new wiring, new walls, insulation for the top floor, polished up the eight marble fireplaces and pulled the ancient sinks out of the former bedrooms.

Then he discovered the convention center wasn't going away. But he was.

Last March the city took the house, for which he had paid $52,000, by eminent domain. The price he'll be paid is still at issue.

Meanwhile, Conn chose to remain, though the buildings around him have gradually disappeared, leaving his tall, thin house standing alone like a solitary sentry.

Then the burglars found him.

Since he works two jobs and virtually all his neighbors are gone, there was no one around to see who took the washing machine and his dryer full of socks.He went down to do his wash on Nov. 21 and they were just gone.

Two days later his shoes and appliances disappeared and the day after that the two suits and the car.

On Sunday, Nov. 25, he heard someone at his back door and looked down from an upper window to see a man raising a brick to another window a story below.

"I yelled 'Hey, get out of there!' and then ran for the phone," he said. Police arrived in time to arrest the man as he walked away.

But yesterday, Conn finally gave up.

"I wanted to let the house down gently, to stay there until the end," he said yesterday as he stood outside watching movers load his furniture into a van. "But I can no longer protect it. I can't keep people from breaking in."

The convention center, he says, may be inevitable, but it isn't wise.

"It will take up a large portion of the city where people should live," he said. "If energy conservation is important, this area should be reserved for housing. The business community complains that business is down, but the biggest stimulator for business is people [living] in the center of the city."

Conn himself is moving to a basement apartment on Capitol Hill, he says, and doubts that he'll ever again in Washington find even a house he can afford, much less one he loves.

But before he leaves the one on I Street he'll shut off the water and drain the pipes.

"I don't want the pipes to burst in the cold weather and ruin the floors . . ." he said. "I don't want it to die before its time." CAPTION: Picture 1, The home of Cary Conn stands between litter-strewn parking lots, at 919 I St. NW., Copyright (c) 1979 By Linda Wheeler; Picture 2, Cary Conn sits in the second-floor living room of the "dream house" he is being forced to abandon.