Robert Redford never won an acting Oscar. So I suppose he's my guess, though I'd be hard-pressed to figure out when he was a drummer. My second guess would be Christopher Reeve.
How about Morgan Freeman? Sean Penn has never won an acting Oscar, but he has been nominated 3 times, as has Freeman.
Penn won for Mystic River, when Robbins won for supporting actor. Berenger seems a good guess. But I'll stand by . . .Reeve.