COMMODORE'S new Amiga A1000 computer was unveiled at Lincoln Center last week amid flashing lasers, rip-snorting jazz, rented tuxedos and rented celebrities, including Andy Warhol, who was there to bestow the first 15 minutes of fame on the machine. Yet even surrounded by all the glitter, the Amiga stood out clearly as the evening's star performer. When it reaches the stores here in mid-September it will be one of the most technologically advanced computers available for the home and business markets.

Whether it will sell is another matter. In the currently turbulent computer industry, even a dazzling machine like the Amiga - it has been described as a color Macintosh that works faster than an I.B.M. PC AT -has to fight for display space in the stores and is not guaranteed success.

Two major hurdles must be cleared if the Amiga is to survive its infancy.

The first is identity. At $1,295, plus $500 for a color monitor, it is too expensive for the casual home user, who may not know what to do with Amiga's impressive horsepower. And as a new, untested machine from a company that has previously sold its products in toy stores, Amiga faces a tough challenge in cracking the conservative business market. Commodore officials vow that Amiga is the flagship of an armada of business products that will transform the company into a major international force in technology.

The second is software and peripherals. About 15 programs will be available at Amiga's debut, but only three are considered to be useful business tools.