I Have A Bolens Transmatic Lawn Tractor Model 660-688. It Doesnt Start At All. I Put A New Battery, I Changed Solenoid And Still Wouldnt Start. Can Anybody Help Me?..

If the solenoid isn't doing it, then it is most likely the starter.  Unfortunately a much more expensive fix.
If you have a tester, you can check to see if there is power going to the starter when the ignition is engaged at the red lead.  If there is power and still no crank...starter.

I have a 660 w/Briggs & Stratton engine. Mine would try to start but sometimes seemed to be binding (only when engine cold). A jump or a little time on a battery charger would get it to start. The problem was the compression release. The fix was a simple valve adjustment.