2004 2.4L Stratus weird start issue
 

I left my wife's Stratus on th parking spot since last Friday. We had a big snow storm here. This morning I shuffled snow between two spots and moved the car to the other one in front of the car. It started with no problem. I turned off the car and than decided to move the car forward a foot or so. The car cranked and cranked and it seemed like it was kind of starting but it would not. It was almost there but wouldn't "catch". When I came back from work I was able to start it with no problem but when I turned it off I was not able to start it again, just like before. Same "symptoms".
Anyone has any idea what it is?
Thank you up front.

Forgot to add that I put a brand new Duralast Gold battery in two weeks ago.