Starbucks began offering coffee drinkers a way to get free Wi-Fi access at its shops on Tuesday, but some customers had a hard time cashing in.

That's because some people were unable to access Starbucks' Card Rewards Web site in order to sign up for the program, which offers two hours of free Wi-Fi access per day to participants.

Some visitors to the site were greeted with a pop-up window stating: "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."

Starbucks announced the new program on Tuesday. People were encouraged to visit the Card Rewards Web page to either buy a new rewards card for US$5 or to register an existing gift card to be part of the program. Users who sign up before July 14 will get a free drink, and everyone who signs up can use two hours of AT&T Wi-Fi access in Starbucks shops free every day.

In order to get the two free hours every day, Card Rewards program users must buy something with the card at least once a month.

A Starbucks spokesman said that the problems were on Starbucks' end, not AT&T's. "Customers overwhelmed the site when joining Starbucks Card Rewards," said Doug Cavarocchi, a Starbucks spokesman, in an e-mail. The problem started in the morning and was solved by midday on the West Coast.

The problem affected visitors in the U.S. and Canada trying to sign on to Starbucks.com with a user name and password, he said, although other users trying to sign up for the program also saw the error message.

The program follows Starbucks' announcement in February that it would begin using AT&T as the provider of in-store Wi-Fi service. For now, T-Mobile continues to operate Wi-Fi networks in some of the stores. Starbucks said that it plans to roll out A&T Wi-Fi in all of its U.S. stores by the end of this year.

The program also follows the launch of the My Starbucks Idea Web site, where anyone can post suggestions for improvements Starbucks might make and vote on other ideas. A week after the launch of the site, which was built on a hosted offering from Salesforce.com, the number one suggestion was to offer free drinks, and number two was to offer free Wi-Fi.