Jonathan Strum might have struck out once with his attempt to give away free iMac computers to people who agreed to sign up for his Internet service, but that’s not stopping him from trying again with a whole new machine.

Strum, chief executive of Santa Monica-based NadaPC, is giving away a compact device that combines television, the Internet and a DVD player. The device, called the iCEBOX, was developed by Seattle-based CMi Worldwide and is manufactured by Samsung Electronics.

The units will go on sale in stores this winter for around $650 each, but Strum plans to give them away for free as long as users agree to sign up for his Internet service for $21.95 a month, plus open a no-fee checking account at Internet bank CompuBank.

For Strum, the only problem now is convincing people to sign on, after his reputation suffered serious damage with the collapse of his last venture.

Last year, Strum headed a company called FreeMac.com Inc., which offered a free iMac computer to anyone who signed up for three years of Internet service provided by Pasadena-based EarthLink Network Inc. There was an enormous response to the offer, with 250,000 people signing up for information on the day the company launched in August 1999.

There was just one problem with FreeMac.com: It never gave away any iMacs.

Strum claims that at the time he started the company, he had a verbal agreement with a regional sales manager at Apple Computer Inc. to distribute the iMacs. But the day after FreeMac.com launched, higher-ups at Apple called Strum and informed him they’d never heard of FreeMac and would not authorize him to redistribute iMacs.

Strum continued to try to get his hands on the computers, trying to set up a deal to buy them at wholesale from distributor Ingram Micro; Apple would have none of it. Eventually, the entrepreneur even offered to buy them at full retail price, around $1,200 apiece, from retailers but Apple officials rejected that, too.

“We knew when Apple could not come through that we had a winning business model,” Strum said. “We knew we had to get some hardware.”

After the collapse of FreeMac in February, Strum began looking for an Internet device whose manufacturer would be willing to let him distribute it. He landed on the iCEBOX, a machine that comes cable-ready and has an internal 56k modem for Internet connection. It plays DVDs and comes with a wireless keyboard, but does not have a hard drive or other storage device like a PC.