Potential battery problems or the other?

i own a 2001 honda accord, to which i finally replaced my old battery, with a new one. The old had trouble starting here and there but it was considered bad. SO after i replaced it after buying it from autozone (the guy said because of my terminals that he couldn't install the battery, one is badly corroded). So after i installed the battery it wouldn't switch over, the car would click and then all electricity stopped. Eventually it randomly started (just when i was about to give up). So it was fine the whole rest of the day, and even this morning. And than stopped, the only way my car will turn on if its 'jumped' and will stay working until i shut it off, then it will need to be jumped again...my friends are saying its my starter (which never gave me problems before..), my starter solenoid, or my alternator..i believe its my terminals...what does it sound like?