stains on older granite

My kitchen counters of Zimbabwe Black granite were installed about 15 years ago. I don't know if they were sealed at that time or not. I have not sealed them since. Within the last few months, some slightly lighter stains have developed near the kitchen sink. They look like liquid might have puddled and stood on the spots. I have tried various kinds of granite/stone cleaners, but have not had any luck. Any suggestions on how to remove the stains? Should the stone be sealed?