I had the same problem with my rear axles not coming out. They really get seized up over time. If you can get one side to come out, you can then drive the other side out with a big hammer and a punch.
I had one that I knew I was going to replace so after pulling on it so hard it came apart like yours did. The way that I ended up getting it off was by drilling a hole in the hub that was stuck in the gearbox and tapping with a 1/2 inch tap. I then screwed some 1/2 inch all-thread (purchased from lowes) into the tapped hole and used a slide hammer to remove the stuck hub.

In about 3 slides of the hammer it broke free.
If and when you do get the axles out, be sure and put antizeeze on the splines of the new/old axles before installing and hopefully they will be alot easier next time to remove.