2002 Oldsmobile Alero wont start

I got up this morning and started my car without a problem. Then about two hours later I tried to start it again with no sucess the first two times. The third time it started and I drove off. About a half a mile down the road it cuts out on me and starts to buzz at me while i'm stopped at a stop sign. The buzzing stopped and I cranked the car up again without a problem. I drive to work without it shutting off again. Then when I go to leave it wont start. Ive checked fluid levels, fuses, and the battery. Do you have any ideas as to what might be causing it? My radiator overflow was empty when I checked it and their was no fluid in the hose that connected to the engine.