When Queenstake bought the dredge, most of the original brass fittings had disappeared, windows were broken and machinery wrecked. Several of the 19 pontoons on which the dredge floated had filled with silt.

Many of the 72 buckets with which the machine scoops up pay dirt had been removed, no mean accomplishment, since each weighs 700 pounds. ''We found buckets all over the place,'' Jeff Lerner recalls, ''some in the bush with trees growing in them. I walked around Dawson and bought buckets from people who had them in their garden, filled with flowers.'' Back in Operation

The Lerners estimate rebuilding cost more than $1 million, but say that building a new dredge, presuming you could, would cost over $4 million.

The refurbished dredge now floats in its own pond, the clanking of its bucket line echoing across the valley. At full power, the line pulls up 33 buckets a minute from 16 feet underwater.

The skill in operating the dredge, says one winchman, is to be able to follow the contours of the stream bed. Because the gold is concentrated in the gravel immediately above bedrock, the first foot of bedrock is scooped up along with the gravel. ''If you dig too deep, you're wasting your time, and if you don't dig deep enough, you miss the gold,'' he says. Two television monitors in the wheel house allow the operator to see what is happening elsewhere on the dredge.

The dredge mines the material and in one continuous process sorts the gravel, recovers the gold, tin and tungsten and spews out the waste, or tailings, in neat piles behind the boat. A Question of Water

Now that the dredge is back in operation, the legal problems have been surfaced.

It takes 5,000 gallons of water a minute to wash the gold-bearing gravel, and Queenstake has run in into difficulties with the federal Water Board. To satisfy the board, the company built three 150-long settling ponds, strung out behind the dredge, to allow silt to settle out of the used water before it is returned to the creek. Coming from the dredge, the water is thick with silt washed from the gravel, but by the time it seeps out of the third settling pond, it is relatively clear.