Did you buy one of the Lifetime warranty crap alternators from AZ, Advance or one of the larger stores? If so I bet the alt is bad. I had had to replace 3 before getting a good one. They use the cheapest parts they can in the rebuild. Their starters are even worse. Now I only deal with DB electrical and I know I have a good unit. Check the voltage that the alt is putting out, should be around 14 volts. Could also be a loose or burnt harness so troubleshoot it.
Good Luck