New alternator not charging battery

I bought a 2002 Pontiac Montana AWD van with tow package drove it home ran fine next day drove it about 10 miles and it started running really bad no power I checked battery was dead, I charger battery and it ran fine for a little while then same thing battery went dead again, everyone says OH it's the battery but I didn't think so because it's a new maintenance free battery so I checked to see how many volts it was putting out when running it was less than 12 volts should have been at least 14. So I pulled off neg. Battery cable it stopped running soon as I pulled it off, so I am thinking it's the alternator, I bought a new not rebuilt alternator ordered it from eBay, put it on and same thing not getting power from the alternator I checked all fuses and relays but it's running straight off of battery. I am going to take the alternator I took off to see if it is bad because the new alternator could be bad but if not what would cause the battery not get power from alternator if everything checked out?