The question of how to sell federally owned Conrail has come down to a simple political contest between Transportation Secretary Elizabeth Hanford Dole and Rep. John D. Dingell (D-Mich.), chairman of the House Energy and Commerce Committee.

If these two diligent, tenacious personalities cannot find a way to resolve what appear to be irreconcilable differences, the chances are excellent that Conrail, the Northeast's prime freight railroad, will remain a ward of the federal government.

Dingell has the home court advantage.

"Conrail is now a lobbyists', advisers' and investment bankers' paradise," said labor adviser Brian Freeman, who resides therein. "It could go on for years. . . . I hope that isn't the case, and obviously we hope there will be a resolution."

On its surface, the question of selling Conrail seems simple enough, a government success story in need of a last chapter. But there are other issues, including tough questions about the competitiveness of railroads, the federal government's need to raise money, and long-term stability for shippers and railroad employes.

Ideology is also involved. Dole has said that the government should not run a railroad, a practice that does not bother Dingell.

The federal government created Conrail in 1976 from the remnants of the Penn Central and six other failing roads. Taxpayers poured $7 billion in subsidies and labor protection payments into Conrail. By 1981, the first year of the Reagan administration, there was agreement something had to be done to cut the government's cost.

Congress responded by relieving Conrail of state taxes, permitting quickie abandonments of unwanted track and spinning off money-losing passenger services to state and local governments. Conrail's employes kicked in with a 35 percent wage deferral.

New management was brought in, headed by L. Stanley Crane, the retired chairman of the Southern Railway, now part of Norfolk Southern. Crane found that the federal money had built a first-class railroad and he used the tax breaks, abandonment rights and new marketing freedoms under railroad deregulation to tighten the screws.

In 1976, Conrail had almost 100,000 employes; now it has about 35,000. In 1976, Conrail had 17,700 route miles; now it has 13,000. Conrail turned its first profit in 1981 and last year it made $442 million. It is paying full industry wages and has $930 million in cash on hand.

Congress also ordered in 1981 that Conrail be sold, in pieces if necessary, together if it became profitable. Dole studied the possibility of simply putting Conrail's stock on the market, but rejected that for several reasons: Anyone could buy and there would be no guarantee that all the stock could be sold, leaving the federal government in a minority position.

But the biggest problem is a view shared by many in the railroad business and at DOT that Conrail -- though profitable now -- is not viable over the long haul because of dwindling population and freight traffic in the Northeast.

"The question for me is viability, viability, viability," Dole said in an interview. So she decided to seek a buyer with "deep pockets." The Santa Fe railroad was seriously interested, and that would have been an easy merger with few obvious antitrust problems. But Santa Fe had to withdraw when the longtime apple of its eye, Southern Pacific, became available. The Santa Fe-Southern Pacific merger is pending before the Interstate Commerce Commission.

Dole kept looking, and found Norfolk Southern. The purchase of Conrail would give Norfolk Southern access to the Northeast, where it had been shut out by Conrail and Norfolk Southern's larger archrival, CSX Corp.

Norfolk Southern agreed to a number of restrictive convenants that would protect shippers, employes, the government and Conrail's treasury. Dole sees her choice as government at its best: a strong, responsible buyer, committed to railroading, providing the government the assurance that it will not have to bail out another railroad.

Norfolk Southern and Conrail have overlapping track west of a line from Pittsburgh to Buffalo, but Dole thought the antitrust problems were solvable. She referred them to the Justice Department for review and asked Treasury to study the tax consequences of a Norfolk Southern purchase.

CSX, of course, has fought vigorously to block Norfolk Southern because a combined Conrail/Norfolk Southern road would be bigger in the East than CSX. Crane, a proud executive who could not get the Southern to waive its mandatory retirement age when he was chairman there, has battled just as hard to make sure Conrail remains independent.

Time and governmental process have worked against Dole and Norfolk Southern. With each month, Conrail looks more vigorous to the financial community, making the viability argument difficult.

Morgan Stanley & Co., a New York investment banker hired by Conrail's management as an adviser, became convinced that a public sale of Conrail stock would succeed and signed up investors to prove it. Another public offering is being proposed by Conrail Acquisition Corp., a joint venture of Allen & Co. and First Boston Corp.

It took the Treasury and Justice departments months to answer questions about the impacts of the sale. Three different divestiture plans of combined Norfolk Southern/Conrail holdings were required before Justice's antitrust division would approve one -- and that one is still under review.

It took the Senate almost a full year to approve the sale to Norfolk Southern, largely because of the opposition of Sens. Arlen Specter (R-Pa.) and Howard Metzenbaum (D-Ohio).

Dole's chances in the House -- traditionally more protective of railway labor and more worried about antitrust issues -- were never better than 50-50. Dingell put Dole on notice in her first appearance before an Energy and Commerce subcommittee more than a year ago that he would want to know everything about the tax consequences to Norfolk Southern, the antitrust issues, the labor issues, everything.

On April 29, after carefully remaining neutral, Dingell said it was time to devise a new plan, that the proposed sale to Norfolk Southern was flawed. "I've indicated after a dreary 14-month wait that my patience is exhausted and they are incapable of coming forward with the answers," Dingell said in an interview.

He apparently expected Norfolk Southern to retreat because, according to sources, his draft press release announced Norfolk Southern's imminent withdrawal. But Norfolk Southern Chairman Robert B. Claytor announced immediately he was remaining in the contest.

Dole visited Dingell and pondered matters. On Tuesday, she asked Norfolk Southern to raise the purchase price from $1.2 billion to $1.9 billion, partly to mute the criticism that Norfolk Southern was offering too little.

Friday, Claytor upped his bid, but by that time Dingell's assessment of a Norfolk Southern purchase had escalated from "flawed" to "dead."

Dingell told Dole, "You have prevailed in persuading me that Conrail ought to be privatized." However, he said, she had failed to persuade him that Conrail's long-term health is questionable.

Lazard-Freres & Co., the investment banking firm advising Congress on the sale, has told Dingell "Conrail has sufficient viability to survive five years."

"The only device which can be accepted here which meets all the concerns we have set forth is a public offering," Dingell said, adding that he did not support either Morgan Stanley or Conrail Acquisition Corp. He praised Dole's efforts and said he wanted a "consensus, bipartisan" solution.

If nothing can be done this year, despite the government's need for revenue, Dingell noted that Conrail is making about $450 million annually. It wouldn't take much legislation to direct some of that revenue to the Treasury.

"I feel no compulsion to make a sale at this time which is going to adversely impact industries, other competing railroads, different regions of the country or which will impair the viability of any competing road or industries," he said. "I'm very content to leave matters as they are." CAPTION: Picture 1, "The question is viability, viability, viability." -- Transportation Secretary Elizabeth Hanford Dole; Picture 2, "I've indicated . . . that my patience is exhausted." -- Rep. John Dingell (D-Mich.); Picture 3, Norfolk Southern Chairman Robert B. Claytor raised bid to $1.9 billion; Picture 4, L. Stanley Crane turned Conrail into a railroad that made $442 million in 1985.