My Tecumseh riding lawn mower will not move in gear. It will not go forward or reverse. What are the possible problems?

Hi,
Tecumseh does not make a mower (Briggs did not until the fairly recent past.) As a rule it is the belt not coming under tension for whatever reason; park brake locked, bad idler, sheared key/sheave, belt out of sheave, etc.
The exception is an MTD product with a Transmatic system. If the machine was shutoff without pushing in the clutch, the belts will wedge in a position that represents where it was when stopped. The pedal will be hard to push, but if a lower speed is selected the next time it is started; it cannot free itself. The directions are inside the hood of most of the newer models.
They are to put in neutral on the shifter (forward and reverse are separate from speed selection on these models) and select the high speed and release the pedal until a whirr of the variable speed pulley is heard. Push the pedal back in, select your direction and things work normally again.
Peace,
Clarke