Up until that week, public looking for free Wi-Fi were reduced to seeking out independent coffee shops that offered the service. That’s been OK for folks seeking to go online in their own communities, but at Starbucks — the ubiquitous purveyor of coffee at airports, shopping centers and on city streets — the cost of World Wide Web access was virtually prohibitive.

Offered through T-Mobile, Starbucks customers could pay $6 an hour or $9.99 a day for Web access. But in February, Starbucks announced it was kicking T-Mobile out of some 5,000 stores in favor of a deal with AT&T. Now Starbucks is unveiling a rewards program that gives Starbucks cardholders two free hours of in-store AT&T Net access.

To use the free service, customers have to buy a Starbucks card, sign up for the company’s rewards program on its Web site, use the card at least once a month, and agree to receive four e-mails from AT&T.

Rewards Site Overwhelmed

Starbucks may not have realized how popular the offer would be. Many customers trying to access the rewards site to activate their service were turned away due to an overwhelmed server. “Due to overwhelming interest in Card Rewards, we are currently experiencing difficulty accessing Starbucks Card accounts. We are working to fix the problem and ask that you please try again later,” a notice on the site said.

“Customers overwhelmed the site when joining Starbucks Card Rewards,” said Doug Cavarocchi, a Starbucks spokesperson. The problem was solved by midday Tuesday.

The fact that the Starbucks site was overwhelmed with would-be customers indicates just how much pent-up demand there is for free public Web service. For AT&T, the deal is part of a strategy to become a ubiquitous provider of broadband.

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