Intermittent won't stop after the initial run for the day

After an overnight parking and I turn on the ignition, the car starts and runs, then when I get to my destination, parked the car and come back say after 1 hour to 45 minutes, the car will start but not run. Left it for another hour, came back and start the car, it runs but when I applied my brake at a stop light, the car died. The car is used once a week only and has about 116,000++ in mileage. Last time I filled the gas was almost a month, still has just below half full, its saturn L300 v6, Y2001