Why does my car turn off when I take off?

I have A 2007 SATURN VUE 4 cylinder....sometimes when I am at a stop and I press the gas to go it stall on me at the middle of the intersection. It begins to chuckle like if I ran out of gas or something and shuts off. Other times it chuckles but then keeps going. I have taken it to saturn and they can't seem to find anything wrong with it. Also, since I'm here my car didn't want to start this morning, all the lights turned on but I had to keep pressing on the ignition for it to start and all you can here was the engine trying to start like if I was drowning it with gas. So I was thinking it was the battery but I don't know, any suggestions?