1990 GrandAm Starting problem........

I have a 1990 GrandAm. It had been sitting for a few months, and I am now starting to drive it. It has a starting problem. It seems to start whenever it feels like it. If I get a jump, it starts immediately, first crank, then after that it will start a few times, (but even sometimes after a jump, it wont start after that without another jump), after that the most times, when you turn the key, it doesn't do anything, won't turn over, but the accessories turn on. I bought a new battery and a new alternator (AutoZone said it was the alternator, but apparently not).

Can anyone help with this problem???

Sounds like your Neutral Saftey Switch is going bad. I replaced mine not too long ago. Its not too hard to change and runs about $15.00.