Car won't start

2002 Saturn S series with 82,000 miles. Four cylinder. The car won't start without jumping it. The problem has been sporadic for the past 5 months in which time I've replaced the battery and the alternator. I replaced the alternator after the car stalled and wouldn't start. It's my daughter's car and she said she was able to get it started once by jiggling the key in the ignition, this hasn't worked for me. When I charge the battery it always starts and will start a couple of times without charging it but then won't start. The problem is getting worse.

Thanks.