Why won't my car start when being jumped?

My car's battery went dead. (So I think). I hit my after market CD player in my car a couple times to get my CD out. Its old. But anyways the CD popped out and several minutes later I went to start my car and it turned over a tiny bit then all my lights went out like my battery was dead. The next morning I had someone come try to jump start it and lights come on and it turns over but wont catch and fire. I asked a few people if they had any ideas and I was told possibly my fuel pump. I checked and it works. Then I was thinkin about when my moms car would not start and the security kicked on when they replaced her heads. I can't figure it out. Have had this car 2 years an never had this problem. Would anyone have any possible idea and or way to figure out what's wrong and how to fix it? Please and Thank you!

BigLoomis