Q: Alternator went bad within a 24 hours of installing it

about a week ago i noticed i was losing power while i was trying to start my car. when i got home it would not start. i replaced the alternator. not even a whole day went by and it was shot. i tried the disconnecting the negative battery terminal to see if the alternator would keep it running. it did not. i know the alternator is bad but im trying to figure out why it would go out in a day like that. i installed everything correctly. although i did notice yesterday while trying to further diagnose, that the power cable connecting to the alternator from the battery came lose and was barely connected to the power source. i did reconnect it with no luck. im affraid to put a new alternator in because i dont want to blow another one but i also have a feeling i may have been sold a reman dud. also, when i turn my turn signal on or roll down the windows, my stereo will flash and cut off for only the time i am using power in another source. also according to autozone my battery checks out fine

My car has 1830000 miles.
My car has a manual transmission.