Quote from Polnareff

Maya is a 3D modeling/animating program...so not quite the same.

I believe he said something like

Is there any other animation program that has nothing to do with flash, EZtoon, And pivot?

So I think Maya would qualify as "unrelated".

I suggest if you DO want to try 3D modeling start with Anim8or, it is very simple.

Here is an entire page of 2D animation software: http://animation.about.com/od/referencematerials/a/freesoftware.htm

Quote from LN3uq

Maya ?

They use Maya for South Park. So there are ways for the 2d effect. Just make your "puppets" 2d.

Yes, but there is a 30 day free trial.
You can dowload a free trial of Flash CS4, when that runs out you can uninstall it, then instal CS3, ect.

This way you can get about 5 months of using flash for free.
I got Flash MX 2004 Pro for $50.

Here are a list of versions of flash free trials:

MX 2004
MX 2004 Pro
Flash 8
Flash CS3
Flash CS4

Flash 8 is the best in my opinion.