When my ground connection to the battery was loose, or when my battery was weak, I always heard that infamous, "zzt zzt zzt clickety" sound too. Double check your ground and make sure it's touching BARE metal on the body side. My ground was haphazardly connected to a painted part of the body, which made for a bad ground.
Jumping your car also grounds the battery, so that would make it start.
Try this: take your battery and put it in another car, if that car won't start, or has a weak battery sign (dash lights dim, clicking noise), then it's DEFINITELY the battery. If the car starts right up, then you need to find a better ground, and from what you described, the car starting up, then a minute later you try to start it, and the car won't start, it sounds like you have a bad/loose ground.
Also keep in mind, that if a battery is REALLY bad, jumping the car will only work for that session only. Once you turn off the car, the car will not start again unless you jump it, indicating a dead battery.