Cranking Problems

Well, I have a problem with my Alero cranking at times. I have a 99 Alero V6. First time this happened i tired to crank it up and it wouldn't say nothing, so i got a boost off. Then i took it to Autozone and they told me it was a dead battery, so i got a new one. Then my charging system light start coming on and i was told it was the alternator, so i got a new. Now the other day i went to crank it up and it'll turn over but it want start. I had to sit there for a while and went to crank it up and it started right up. Would someone please help me. I'm a woman that knows a little about cars, but i don't know what could be causing this problem. :confused: