89 Accord Batt Light (Please Help!)

Ok, I am here seeking technical help in diagnosing a specific problem
with the charging system in my car.

I have an 89 Honda Accord DX, carbureted.

My battery light has been coming on intermittently. This weekend, I
installed a new battery, a new alternator and a new fuel pump. This
morning I was driving to work. At one point, the light flashed on and
off with the blinker light. Eventually it stayed on. If I turned off
all the accessories, then it would go out, until I got closer to work,
then it stayed on. I noticed all my lights were dimming, like the
battery was being drained. After I arrived to my parking spot, I shut
it off, and tried to restart it. It would not start, barely cranking
over...

So, my if battery is new and the alternator is new, why would my
battery be dead after a short (20 minute) drive to work? Is there
something I am missing here?