Blockbuster Inc. will start renting movies and television shows through a new gadget that may give consumers another reason to bypass the struggling video chain's 7,500 stores. The new system announced Tuesday relies on a small box that connects to television sets and stores video after it's downloaded over high-speed Internet connections. The player, made by San Jose-based 2Wire Inc., is built on the same concept as storage devices made by Apple Inc. and Vudu Inc. The devices are all meant to provide a bridge between the Internet and TVs. Netflix Inc., a Blockbuster nemesis, has been trying to make the same leap with a video-streaming service that can be watched on TV sets through a variety of devices, including a $100 box introduced by Roku Inc. six months ago. Blockbuster's foray into so-called "on-demand" video also pits the Dallas-based company against instant-gratification services already offered by major cable carriers like Comcast Corp. and Time Warner Inc.