2004 Ford Explorer XLT not starting.

One day I was driving and the suv went into limp
mode or was losing power (idk), I tried to turn on
after shutting it off and it wouldn't start. Next day I
come out ti a drained battery and a dead
alternator. I replaced the alternator and also did a
tune up (as it needed both). So I charge the
battery, all the typical lights come on in the dash,
but I hear a long beep for a couple seconds after
trying to start it. When I try to start it, it acts as if
though the battery is dead...and it's not. I hear no
clicks and the dash needles stutter for a few
seconds.I don't what is going on.