Auto Parts: 96 integra i think electrical problems?, load tester, battery terminals

Question
First off heres the story got a car yesterday, drove it around fine first day started it probly 3 times. car started again today. then couldnt get it when i got home and went to go start it again. wouldnt start got it jumped 3 different times through out the day took it to autozone said it was a bad battery. so i got a new one car started up good, got home tried to start as soon as i shut it off and once again wont start. their are 3 wires into the positive on the battery and one on the negative. i know it has an alarm and a deck. i have no clue what it could be. please help!

Answer
    First of all, let's be clear what we mean by not starting.  Does it not crank at all (engine does not turn when key is turned)?  That's going to be either the battery or the starter.  If you turn the key to start and hear a rapid clicking noise, then the battery is low or dead or the cables are bad.  If you hear nothing, then the starter itself is most likely bad.  However, if there is something (like an aftermarket alarm or stereo) that is draining the battery, the battery could be completely dead and would act like a bad starter.  If you take the starter off (not really that difficult on these cars), you can take it to a good parts store and they will be able to test it on their starter tester.  If they say it is good, then start looking elsewhere.  If you have a voltmeter, check the voltage across the battery terminals with the cables off, and then with them on.  A fully charged battery should be around 12.7 volts with the cables unhooked.  If it's below 12, then it needs to be charged.  If you charge it and it's still below 12, then the battery is bad.  Yes, new batteries can go bad, and the guy who sold it to you should have a load tester with which he can test it.  If you hook the cables up and the voltage across the terminals is below 12, there is probably something either shorted or not turned off.  Diagnosing this will be difficult.
    If by not starting you mean that it cranks but won't fire, well, it could be anything.  But, my experience with Hondas of this ilk is that if they crank but don't start they need new spark plugs.  Don't know why, but have run into this several times.