Would pulling on the speedometer cable tell me if its broken?
 

I unscrewed my speedometer cable and put a pair of pliers on it and I can pull on it and it has at most 1/2" of play but I cannot pull it out of the sheath. Would this indicate that it is not broken? When I drive, it does not spin as I put it in the cabin, I am stumped.

Probably fuzzed-up on the broken end, and binding on the liner. Definitely needs to be replaced if not turning!

Did you pull on both ends? Did you check the drive gear with the car in the air and the trans turning?

Milt, no I pulled the speedometer and put the cable through the hole. While driving it does not turn. However I cannot pull it through the cable housing. I am confused as to what the problem could be?

Try removing it from the transmission end.
I am guessing that it has broken and split apart inside the cable housing causing it to catch as you try to pull it out.

To replace it do I use the old housing to pull through the new one? Which side of the transmission am I looking at to to remove this cable?