Car hesitating

Hi there. I have a 2005 vw jetta 1.8 turbo, manual. We just got the 5th biggest snow storm in brooklyn's history. Before the snow, my car was running perfectly. It was snowed in for a week and caught in a major snow drift so most of it was covered. I just drove it for the first time and it hesitates now when accelerating. After driving it for a little while, the check engine light also came on. What could have happened during that storm? It almost feels like something is caught in the transmission. It is still perfectly still while idling. Help!