Model #s may be of help. You want to confirm that both wheels are locked to the axle. IE is the square key in place. Does there seem to be good tension on the belt?

Was the "shredded belt" still in place before you replaced it? or was it chewed up and spit out being a loose piece of rubber?
Either way there is a possibility that the new belt is not routed through its pulleys properly, and therefore is not tight enough to drive the trans input pulley.
If the new belt is not the identical OEM belt it might be a bit too long which will also cause inadequate tension in the pulleys.

My feelings about using hardware store belts is: You will spend much more cash by buying a belt that "looks about right", but isn't, and if ya have to drive 5 miles in both directions, you might as well have gone to the dealer, or a reputable repair shop, and saved a lot of down time! Invariably, the hardware store belt won't be correct, and will require many trips back and forth to finally/maybe get one that will work!

I took the shredded belt to the place that I purchased the mower and they used the number on the belt to get me a new belt. I put it on and it is tight to where I can not make it slip if I try to hold it. I am wondering if it is like tomplum mentioned if there is a keyway that isn't there? I had to take one of the pulleys off to put the belt on and i am going to look tonight if when I put the pulley back on and tightended the nut that it is just enough to turn the axel but not hold the axel. to me to break a belt wouldn't break a tranny? Thanx for the input everyone.