I was able to push start it. The starter clicks but can't start. I changed the starter, made sure there was no corrosion on the battery terminals. Charged the battery.

the battery terminals are not always the problem. its the connections on the cables themselves,,,,the point where the thick copper wire goes inside the clamp --the one you put on the battery. Try this--get a spray can of wd40 and soak the stuff into the copper wire /clamp connection point. get it inside. then try to start the car. Its a temporary fix--for how long i dont know.
http://answers.yahoo.com/question/?qid=20080605162234AARQ731

I'd tow it to a shop and have a professional PROPERLY diagnose it for you.

Well,
You've already replaced a starter which must have set you
back $ 75.00 or more.. Let's not replace anything else before
you have diagnosed it further or as stated by another, got
some professional advice. You can't charge a battery that
doesn't have the capacity to hold a charge anymore. Sure the
starter may have been the culprit in the first place but it sound
like it may have been your battery the whole time. If that battery has quite a few years on it, chances are you are only
holding a surface charge and not fully charging the cells.
Even if you get a jump start from a friends car, it may not
start if your battery is that far gone. Try switching out the battery or buy a new one, When you jump start the car using
the transmission, chances are, it's running off the alternator
which you can fry too if it's overworked..
Just another opinion here....