I have a Toro 22" recycler mower with 6.5 HP Tecumseh engine. The other day it just stopped on me while using it. Now the pull cord will not budge. I can turn the blade by hand, nothing is blocking it. I removed the housing and when I lift the pully system out, the cord will pull out all the way. It just won't pull at all when it's on the mower.

You can move the blade by hand and you can pull the cord if the pull station is removed from the shaft.?
well. there is a "not too complicated " way to see whats going on. Try taking the spark plug boot off....and the spark plug. then stick something safe" Lets say a drinking straw" into the spark plug hole.....next lets turn this lawn mower blade and see if the blade and crankshaft are all still in one piece.
If the straw goes deeper and then pushes back out...then the blade to crankshaft check out ok. if not..then the engine ceased and broke the blade shaft..(thus blade moves while motor and cord doesnt)
Now if they both DO move properly then i would observe the screen that covers the cord (that screen that spins while its usually running) and see if that moves in sync with the blade moving.if yes i would suspect the magneto has spun a bearing. if it doesnt move then i would suspect a broken shaft between the motor and the magneto . What puzzles me is that you say it was running when it went dead and been locked up since. Which kinda points me to a locked up Magneto. which is too hard to pull by hand but still can be moved by the blade (moving the blade has more leverage than the pull cord-- little circle and big circle type of leverage) You can replace the Magneto if you order the parts. (and borrow the neighbors lawnmower for a couple of "mows") Which is secured to the shaft by bolts and screws. and a "key" on the shaft (which also makes it stay in alignment) relatively simple to do if you are handy.
Hope this helps you out to get started.
post more info as you make discoveries and we can continue to help you out
Good Luck!

If the piston isn't going up and down when you turn the engine, the motor needs some serious major internal work or can be considered junk. likely a broken connecting rod.