It may be the starter itself. If it runs with a pull rope then it is not any kind of engine trouble. Your best bet may be to replace the starter itself and see if that works.
It sounds likely that the battery for the mower is dead, or has too weak of a charge to start the mower. Try charging the battery for a few hours and see if it starts; if it still doesn't it likely needs a starter or starter solenoid.
If your mower starts with the pull rope, you could have a dead battery, a loose connection or a worn out starter. Have your dealer check the electrical system.
the battery could be going bad or the starter getting weak. also, the wires to the starter may be loose and need to be tightened. check the charging system to see if it is working.