changed battery but battery light still come on when car is turned off

I went to a well-known store to have my old battery checked. I was told that it was dying because it would not hold a charge. If the car is off for more than 10 hours, then it would not start. with the old battery, I was also told that the problem is not the alternator because it charges the battery when the car is running and driven for some minutes. A church member told me that the alternator diodes might be going or gone bad. So, I bought a new battery and just had it installed. The terminals are properly connected, and the battery is in place, when I start the car, the battery light goes out, but comes back on after the car is turned off. Why is that happening? Is it the diodes?