1996 Toyota Corolla smoking

My windshield was frozen over so I turned on the defroster and scraped off my car. My car began to make a funny sound and then began smoking. Once I turned off the defroster my car was fine. Yesterday night however coming home my car died. I was able to restart it and got into the parking lot of my apartment complex and it died. The battery and oil lights came on however I got it restarted. This morning it started fine. I was wondering if it could be the fan belt. I checked the oil and it is full.