Chevrolet Repair: Battery/Alternator?, positive cable, alternator belt

Question
I have a 99 Cavalier, I bought a battery about 2 months ago because the battery would not hold a charge, it's doing the same thing again. the car will start when you jump it but after about 20-30 minutes it will not start again. No lights, no nothing. I dont know if it's the battery, the terminals or maybe another part and no seems to know what it is. I don't want to buy yet another battery if that is not the problem?
My second question. the check engine/track off light will come on every now and again, stay on for a week or so then go off, then a few weeks later come on again, and again, no one seems to know why?
Can you help me with these two issues?

Answer
Hello Susan..Let's fix your car!The cavalier has a charging system that has a wiring harness...a group of wires...that go down in front of the engine behind the front engine mount.When you look at the starter you will see 2 0r 3 wires that go to the same terminal as the positive cable from the battery.Both of these areas are of a concern on a Cavalier.I need you to do a couple of things....1)When the vehicle is running,you,or someone you know that can read a ''voltmeter'', should check the voltage at the two terminals on the battery.There should be 13.8 to 14.2 volts at the terminals.Now...2) When the vehicle is shut off...the battery should have a reading of 12.6 If the charging system is not working properly you will not see 14.2 but the same 12.6 you saw when the vehicle was not running. This tells me that the charging system is not working and that after you run the vehicle for a while and shut it off the battery is ''dead''...Why...Because you are depending on the battery to run the electrical components on the vehicle and the battery is only good for about 1 to 2 hours depending on the accessories you use...Headlights, Radio, Air, The more you use the less time you have to drive. The alternator sustains the vehicle for the most part after the vehicle is started. A very loose alternator belt will also allow the battery to discharge fast..So find a meter and a friend and check it out...Oh yes ...the light on the dash...Probably a shorted diode trio or rectifier bridge..It probably needs an alternator.....Best