dreadseb

This weekend I had drove my FC out to the mountains to go snowboarding and it was drove great on saterday morning on the way to and from the mountain but in the afternoon I went to take it to pick up some dinner and it died on me whenever I had to stop, but as long as I kept my foot on the gas a bit it was alright, and when it did i would have to leave it for maybe 5 minutes before it started up again. Then on sunday I had to get it back home and the only thing that would successfully get it started due to the battery startin to get weaker was push starting it, then about 20 minutes from home it died on the highway and didnt want to start again. I'm thinkin it might just be my fuel filter is plugged up or maybe my fuel pump crapped out but this is my first 7 and I was wondering if you guys have any suggestions about what else I might be running into here?