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”The Big Easy” (Dennis Quaid, Ellen Barkin; Jim McBride, dir. HBO, 1987; color. Running time: 100 minutes. Rating: R. $89.95.)

There`s something rotten in the New Orleans Police Department, and the prissy assistant district attorney (Ellen Barkin) plans to discover it.

Perhaps it`s the studly young detective (Dennis Quaid), who seems more intent on having a good time-and Barkin-than solving a series of murders.

Or perhaps it`s Quaid`s fellow cops, who keep popping up on the wrong side of the corpses.

But, ultimately, solving the crimes and uncovering the corruption isn`t the driving force behind ”The Big Easy.” The driving force is passion-and what drivers Quaid and Barkin are.

Quaid is the pretty one here, the cavalier cop who`s so wrapped up in his own charm that he can`t recognize the scum around him. Barkin is the ugly duckling, the strictly-business woman who`s as sure of herself on her feet as she is unsure of herself in bed.

Though both the thriller and the love story elements of ”The Big Easy”

have their twists, it`s the subtle turns of mood that made New Orleans the Big Easy and ”The Big Easy” a big-screen hit.

No car chases through the French Quarter here. New Orleans stays where it belongs, as the backdrop (albeit, a terrific one) for mankind`s two great desires-money and love.

And you don`t, as happy video consumers should discover, need a big screen for that.