Have an electrical contactor single phase 220v. Contactor works when ingaged by hand.But if pushed by the pushbuttons then the contactor won't ingage.What is wrong with the push buttons that they won't work?

Bad start/stop station
Bad coil
Broken wire
Bad splice
Open control circuit

From where I am sitting it is very hard to tell.

Do you have a tester? How skilled are you at troubleshooting electrical?