When I turn on the ignition my car will not start

I have a 1998 4 cyl. Nissan altima w/ approx 89,000 mi. When I turn on the ignition my car will not start. It doesn't even make that click-click noise like it's trying to turn over. It's just dead quiet. I have cleaned off the corrosion on the battery and tried to get a jump-start but the car still does nothing. The interior and exterior lights work. So does the dash, radio, power doors and windows. I didn't leave any lights on by mistake. I had the alternator replaced less than 2 years ago. I was hoping it was something simple like the battery, but it seems like it's something more complex like maybe the starter or some other part. I would appreciate any suggestions on what it may be and how to repair it. Thanx