Nissan Repair: Problems starting my 95 nissan maxima, nissan maxima, pep boys

Question
I had the car checked out at pep boys and they told me that the battery was bad and I needed a new one before they could check the alternator. I then decided to ask my friend for help. He brought a charger and a voltmeter. After charging the battery for 5 mins with the car off, the car started up with no problems. He checked the battery voltage and it registered above 13 volts. We waited a few minutes to see if the voltage would drop significantly, it only dropped to 12 volts. I then took the car for a quick run up and down the street and he tested the voltage again, it jumped back up to 14. We did this over and over for a good half hour or more and got the same results. The battery was charging, so it means there's nothing wrong with the alternator or the battery. Any ideas?

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Followup To
Question -
My car died on my last night when I got to the supermarket. I had just parked the car and I hadn't even switch the car off yet. Everything just shut down. At first I thought it was the battery,  but the lights still came on (I had my battery replaced in January of this year because the mechanic told me that the previous battery had a defect and couldn't hold a charge, but what are the chances that this battery is also defected?). I had my car jump started with my cousin's battery and everything seemed to work fine and I let the car run for a bit. But after a while, when I was pulling out of the parking space, it dies again.
I keep needing a jump to charge my battery off my cousin's car to get home (the airbag lights is on too). We tried connecting both car batteries with his car off. I started my car up and it worked. Is it a problem with the battery? The alternator? The battery cables?

Answer -
Mike,

Have the battery tested first.  If it is good check the alternator.  And, it could be the cables if the battery and alternator check good.  From what you have said I think the battery is defective and shorting out internally.  

Answer
Check to make sure that the cables are tight and since you are having proper output on the alternator and battery you should be good until the alternator goes out all together.  Sometimes the brushes get into a bad spot as they wear and the system refuses to charge.  But, for the time being my bet is corroded or loose cables.