Battery Light Still Comes On

Here's the the little problem that turned into a big
problem and more money coming out of my
pockets. I had 1 dim head light, I replaced the
bulbs and the lamp but it still showed dim, I had a
mechanic come too look at it, It was the wires he
said, He fixed the light by attaching the wires to my
battery, Car ran good for bout 3days now its
shutting off and now the battery light is on. I asked
him is them lights killing my battery he said no it
has to be the alternator, Bought a brand new
alternator battery light still on, Bought a brand new
battery light still on, Figured it was the headlights
so I untached the wires that was attched to my
battery, Battery light still and sometimes it doesn't
crank on the first try. Im so frustrated and
confused. Someone please help.