When the stock of America Online Inc. sank to $82 a share early last week, all the AOL watchers had ready answers.

AOL's profits, the best of any Internet company, would soon be blown away by a price war. AOL's competitors in Britain were already offering free Internet connections and the trend would sweep America, starting with big price cuts by Microsoft Network.

At the same time, high-speed Internet connections--using telephone lines or television cables--would soon race past AOL's conventional modems. The cable and phone companies would conspire to control the faster format known in Net jargon as "broadband" and AOL would be left out in the cold.

AOL stock has rebounded $30 since then and the AOL seers are citing the very same reasons: Internet pricing and broadband service.

Only now, both those factors are supposed to be working in AOL's favor.

Instead of launching a price war, Microsoft Network last Friday announced it will raise its monthly flat rate fee from $19.95 to $21.95--the price AOL already charges for unlimited access.

And instead of being left behind by high-speed Internet access, the guess is that AOL will set the pace by making a deal with Excite At Home Corp., the biggest provider of cable Internet connections, and AT&T Corp.--which is not only the biggest long-distance phone company but also the biggest shareholder of Excite At Home.

Speculation about an AOL deal with AT&T and Excite At Home made its way through the AOL mavens earlier in the week and yesterday hit Wall Street, boosting Excite's stock $5.06 1/4 a share to $43.43 3/4. AOL shares fell 62 1/2 cents to $109.25 as traders cashed in some of the profits they made when the stock jumped $22 in the five preceding days of trading. AT&T stock--too stable to be rocked by market rumors--closed down 25 cents at $43.50.

AOL executives wouldn't comment on the rumors yesterday and analysts close to the company dismissed speculation that a broadband deal with AT&T is imminent.

"They could do it any day," said Ulrich Weil of Friedman, Billings, Ramsey & Co., emphasizing the "could." The hang-up, he added, is whether AOL wants to let AT&T Chairman C. Michael Armstrong dictate the terms of any agreement.

Armstrong has invested heavily in building high-speed Internet connections--"the big pipes" as Weil and other analysts like to call them. "As the pressure mounts to fill the pipes Armstrong is building, the only one that can really help is AOL."

But Weil said there is no rush for AOL because "there is no massive demand out there to pay an extra $20 a month" for high-speed service. Customers are reluctant to pay that much simply to have Web pages pop up on their screen faster, he argues.

But the new 5.0 version of AOL's software, which is scheduled to be released next week, will have features that take advantage of speedy connections to provide better-quality video and music over the Net. Within 60 days AOL will start promoting high-speed service via telephones using DSL (digital subscriber line) technology, Weil predicted.

Part of the reason for the rapid rebound in AOL stock was "that it was totally oversold," he added. "Investors were gripped by paranoia over all kinds of fears that had no real substance behind them. AT&T was not going to eat their lunch. AOL was not going to die from free service."

Noting that AOL is still well short of the $146 high it hit in the spring, Weil said he now expects the stock to approach that price within the next 12 months. That's assuming normal market conditions, he added: "If the Internet were to run wild again as it did last year, then it could easily go back and surpass its former height."