Hard Start after replacing Alternator and Battery

I've got a 5.7L Hemi that has
been having the battery light
come on while driving and
would have a hard time starting.
A few days ago, it died while
driving and would not start
without charging the battery.  So
I changed the alternator and
after charging the battery, I
started it and it ran fine.  When I
tried starting it again, it was
having a hard start.  Pulled the
battery and it was leaking
battery acid, so I got a new
battery.  First time starting it, it
had a hard start but ran fine
afterwards. Turn it off and then
try to start it again and it acts
like the battery is dead, just like
before.  What are possible
problems?