Battery and brake light flashing?!

So, my battery and brake light
started flashing on and off. Random
periods of time when they stay on
and go off. Then my headlights
would start dimming. I figured it was
my alternator and so I went to get it
checked. The alternator and the
battery are just fine. One battery
cable was kind've corroded but I got
that fixed. Then on the way to work I
stopped at a stop light the lights
came on and then the car turned off.
And now it won't start. Any
suggestions as to what it is??!