Richard and Gloria Randall always wanted to see the countryside by train. So, with a sense of adventure, the New Jersey retirees boarded Amtrak's Broadway Limited for their journey from Chicago to Trenton, N.J.

Their hearts sank almost immediately. Bags of garbage were piled in the rear in their car. At night, there was no heat in their coach car, and the Randalls shivered for hours. And as they were trying to fall asleep, the train slammed to a screeching, and never explained, stop in an Indiana cornfield. ``It was the pits,'' recalls Mr. Randall, a former truck driver.

After years of neglect, Amtrak's long-distance trains are plagued by breakdowns and delays, running late almost 40 percent of the time. Last year, Amtrak received 70,000 complaints about shoddy conditions ranging from dirty bathrooms to rude personnel. That was twice the number of complaints six years ago.

Many 20-year-old trains lumber into stations with taped-up windows and peeling interior paint. Recently, Amtrak director Robert Kiley admitted that when he tried using the fold-down sink in his sleeping compartment, it came off in his arms. ``We're like a leaky bucket,'' concedes Thomas Downs, president of Amtrak. ``We should have plugged the leaks long ago.''

The problem is money. Since the 1980s, Congress has tried to reduce or modify federal subsidies to Amtrak, hoping to turn the quasi-government outfit into a self-sustaining company. Clearly, the experiment hasn't worked; in its current fiscal year, Amtrak is coming up $200 million short on a $2 billion budget.

Meanwhile, ridership continues to decline just when Amtrak needs it most; in fiscal 1994, ridership fell 6 percent on long-distance trains. The outlook for this year isn't much better, despite a general rise in travel.

In the face of these problems, Amtrak is considering several responses _ expected in April _ which may only further alienate riders. It is aiming to cut back train-miles traveled by 20 percent, for instance, in a system that already has major gaps. For example, getting from Atlanta to Miami requires a 1,200-mile detour through Washington, D.C.

Combine new reductions with existing service woes, consumer experts say, and train travel could vanish as a viable alternative to planes and buses. ``It's not just Amtrak service that we're losing but an acceptable form of mobility in smaller towns and cities,'' says Michael Ashington-Pickett, editor of a travel newsletter in Orlando, Fla., bearing his name.

What makes Amtrak's current problems appear so jarring to some travelers is that the company still manages some transportation jewels. Some long-distance trains such as the Capitol Limited and Auto Train are being outfitted with spacious new double-decker cars. Metroliner service in the Northeast has been upgraded with dinettes and telephones, as well as first-class cars dubbed Metroclub. Metroliners couldn't be much more reliable, zipping between New York and Washington at 125 miles an hour, 90 percent on time.

But take a ride on Amtrak's Coast Starlight service between Seattle and Los Angeles, and you're on a train that's tardy 60 percent of the time.

Indeed, Peter Lichtenfeld has found that when he uses Amtrak, it helps to fly. The Jericho, N.Y., neurologist and train enthusiast recalls that the Amtrak train he took from Denver was running six hours late. So he left the train in Omaha, Neb., got a cab to the airport and caught a flight to Chicago. He arrived there in time to make his connection with an Amtrak train to New York.

The average Amtrak car is 22 years old. Some even date to 1948, a jolt for passengers who climb aboard with the scenes of travel comfort pictured in Amtrak ads dancing in their heads. Passengers ``tell you how ugly the train is,'' says Joseph Andelfinger, a Broadway Limited attendant. Amtrak says it will be able to retire its oldest passenger cars as the service cutbacks are implemented.

In one of the Broadway's coaches, passengers stare at a row of TV screens showing ``The Client.'' But they can't hear the movie, because Amtrak didn't stock headsets. When passenger Charlie Gallanti inquired of an Amtrak employee, he was informed that unless he had his own headset, ``It's a silent movie.''

But the biggest problem for many passengers is that Amtrak isn't very convenient. Most of the system is a single train a day in each direction so that trains reach some cities in the middle of the night. Some stations are badly located. Amtrak passengers arriving in Syracuse, N.Y., for example, find themselves a 15-minute cab ride from downtown. In Atlanta, the station is a two-mile trek to the city's center.

And Amtrak already doesn't serve some important travel markets, including Dallas to Denver and Atlanta to Chicago.

Cyndae Arrendale Bussey of Atlanta says that she and her husband, John, wanted to take a romantic train trip to Miami several years ago. Undeterred when they discovered there was no direct Atlanta-Miami train, the Busseys drove five hours to Savannah to board an Amtrak train _ which arrived an hour late. ``Nobody in their right mind would do that,'' Mrs. Bussey now says.

For all its woes, Amtrak has many supporters. They praise Amtrak seats that are far more comfortable than airline seats and big windows from which they can take in views of mountains, coasts and farms. Some business travelers say they can work well aboard an Amtrak train.

Charles Hunter, a music manager from Chesterfield, Mass., will go out of his way to use Amtrak, even on long trips. Mr. Hunter, who represents folk musicians around the country, once took Amtrak from Springfield, Mass., to Austin, Texas, a journey that required four trains over 72 hours. The trip was exhausting, concedes Mr. Hunter, who nevertheless enjoyed the challenge. ``At its best, rail travel is exhilarating,'' he says. ``It is more like a sporting event.''