Transportation Secretary Elizabeth Hanford Dole's plan to sell Conrail to Norfolk Southern Corp. for $1.2 billion was all but officially killed yesterday when Rep. John D. Dingell (D-Mich.) announced that a "new plan must be devised."

Dingell, chairman of the House Energy and Commerce Committee, which would have to approve the transaction, said in a late-afternoon press release that the sale "is mired in a hopeless swamp of confusion and controversy" and "the administration has failed to establish that its proposal is in the public interest."

In the Senate, where Norfolk Southern's purchase of the federally owned Conrail was approved Feb. 4, sources said that Dingell's position probably ends any chance of that sale.

Dingell had remained neutral on the issue until yesterday, when he met with with Norfolk Southern Chairman Robert B. Claytor before releasing his statement.

Claytor said in a statement: "I am, of course, disappointed. . . . We continue to believe that our proposed acquisition of Conrail is in the best public interest. . . . Accordingly, our offer remains open, and we hope the House of Representatives will give it the same careful and favorable consideration the Senate did."

Dole has battled for more than a year to win endorsement of her selection of Norfolk Southern to acquire Conrail. She said in a statement that "Mr. Dingell has expressed his specific concerns about the Norfolk Southern proposal to acquire Conrail and he has yet to see the evidence which he requires to support that proposal. I believe we can address all of his concerns."

She did not address Dingell's offer to work out a consensus. However, Dingell laid down conditions that have been unacceptable to Dole. He said that "any new plan should preserve Conrail as an independent entity and afford the public a fair opportunity to participate in the ownership of the railroad."

Dole and her lieutenants have said that Conrail must be part of another railroad or strong company if its long-term survival is to be assured, and that a public offering of Conrail stock could not be arranged in a way that would guarantee both Conrail's future and a permanent, stable divestiture of government ownership.

The federal government owns 85 percent of Consolidated Rail Corp., Conrail's official name. The rest is owned by an employe trust. Conrail is a freight-only railroad created by Congress in 1976 from the remnants of the Penn Central and six other floundering Northeast railroads.

In its early years, Conrail consumed more than $7 billion in federal subsidies and labor protection payments. Since 1982, however, Conrail has been making money.

Last week, Conrail Chairman L. Stanley Crane testified on Capitol Hill that Conrail has $939 million in cash and that the railroad's pension plan is overfunded by $360 million, for a total of $100 million more than Norfolk Southern has offered to pay.

Thomas A. Saunders III, managing partner of Morgan Stanley & Co., which has sought approval for a public offering financed by private investors, said he was "encouraged" by Dingell's statement and hoped to "have the oppportunity to work" toward such an agreement.