Car won't start, but it's not the battery. HELP!?

About a week ago I noticed that my car would immediately die when I tried starting it unless I put my foot on the gas pedal right away. Once it started, it ran fine. It began doing this maybe a couple of times in the first few days but became more frequent in the last couple of days, and even began doing it after having driven on the freeway when I would come to a stoplight and idle. Last night it completely died. I tried jumping it, and it didn't work. Tried checking all of the connections to the battery and that wasn't it; the problem is that it won't turn over. I just recently replaced the battery and the alternator. Perhaps it is the starter? Or something else? It's a 93 Nissan Sentra Se-R..