Car dying in the middle of the road

salil

I own a Mitsubishi Eclipse Spyder 2008 and had a brand new battery installed on Saturday. Today my car stopped all of a sudden while running. I was trying to get it jump started but when all of a sudden all my lights and everything came and I was able to start my car. I drove to my next destination and the car won't start at all. A friend of mine gave a jump start and my car able to start. I went to the store that sold me the battery and my car died again. This time even though I had a car give me a jump but it won't start. We gave in about 10 minutes and but then suddenly the lights turned on and the car was able to start. Wondering what is going on with my car? Is it the battery or is it the alternator?