Alternator?? Battery?? Or??

So last night I was coming home from the gym my
car head lights started dimming on and off until
they finally turned off, Abs light also came out.  This
morning when I went to turn the car on the first and
second crank failed it was cranking/clicking, but no
start. On The third attempt it started, I noticed that
when I turn on my headlights and roll down the
windows the cars battery gauge goes down. I also
noticed that when I step on the brakes while parked
the cars battery gauge drops and the rpms Jump
up and down slightly. I took it to autozone and they
said both the battery and alternator are good. The
car is starting every time on the first attempt now,
but lights will still dim, abs light will still come out
and its doing everything else I listed. Any ideas??
Thanks