You can't make a silk purse out of a sow's ear. You can lead a horse to water, but you can't make him drink. And unless you have a lot of connections, you can't see a brand new Sly Stallone movie at 4 o'clock in the morning.

Warner Bros. doesn't have any control over the first two things you can't do, but today it makes the third possible. For the first time in many years, a studio will be opening a new film in around-the-clock screenings. Warners calls it a "Cobra-Thon," and the picture in question is, of course, Stallone's "Cobra."

The 24-hour showings are taking place today in New York, Los Angeles and Chicago. Nine other cities, including Washington, get a smaller treat when "Cobra" jumps the gun with 10 o'clock showings tonight, a day before its official release. All those extra showings won't add substantially to the first weekend figures for the film, but that's hardly necessary -- it's something of a foregone conclusion that Stallone's latest shoot-'em-up escapades will top the national box office charts this weekend anyway, especially since it's opening in lots more theaters than its toughest competition, "Top Gun." Dylan in the Wind

Sixteen years ago, Bob Dylan wrote a song in which he rhapsodized about building a cabin in Utah, fishing for trout and raising kids -- "that must be what it's all about," he concluded. Now Dylan will get his chance to play that role. The singer/songwriter has been signed by Lorimar Pictures to star in "Hearts of Fire," a drama about a 1960s rock star who gives it all up to become a chicken farmer. The $12-million feature -- directed and written by the "Jagged Edge" team of director Richard Marquand and screenwriter Joe Eszterhas, and costarring Rupert Everett and singer Fiona -- is being described as Dylan's first "major" role since 1973's "Pat Garrett and Billy the Kid," which apparently means that Dylan's four-hour flop "Renaldo and Clara" wasn't major. Dylan may write songs for the new film, and Lorimar says he'll definitely sing. Deals Down Under

Things are looking up Down Under: The Australian smash "Crocodile Dundee" has picked up its first stateside rave reviews. The Australian government has announced that, contrary to film business fears, it plans to retain the substantial tax breaks that have made movie and television productions attractive shelters. Australian filmmakers had a stronger presence at Cannes than ever before. And Australia's UAA Films has just announced a distribution deal with Warner Bros. in the United States. The first UAA film to be released by Warner will be "Quigley Down Under," an adventure story about an American's encounter with Australian aborigines. Written specifically for Tom Selleck, it won't start filming until next March. Film Clips

As expected, "Top Gun" topped the national box office charts over the weekend. The flashy aerial saga made $8.2 million with almost $8,000 per screen. That's easily the best per-screen average of a major 1986 release, but there's always another statistic around to put things in perspective: It still didn't make as much in its first weekend as "Police Academy 2." According to the L.A. Herald Examiner, though, it did prompt a spontaneous audience sing-along to "You've Lost That Lovin' Feeling" as the final credits rolled in one local theater. The song is sung by star Tom Cruise and his flyboy pals as part of a crucial seduction scene . . . "Top Gun" will face more competition this year than it would have had in previous years: The 55 nationally distributed films due out this summer are 15 percent more than last summer's total. And last year's total was a full 25 percent above 1984's.