2004 Chevy Cavalier cacalidic converter

For the past month my car has been sitting gaining great snow piles on it, and it is partly due to the converter. It glowed red after we drove for a bit, then when we stopped because of the burning steel smell, we noticed that the converter was red hot1 then it refused to start running again. It will start but it refuses to stay running. What could have been the original problem? Before we got the red hot converter? And can the converter be taken out all together and just a straight pipe be put in instead?