The biggest reason we find for this problem is that the safety or kill switch lanyard has been pulled off and the engine kill switch is in the off position. Refer to your engine operators manual for proper operation of safety kill switch.
The second biggest reason we find for an outboard motor to only run for a while or not to start is the fuel line is not plug in or is not fully pushed in to allow fuel to properly flow to the outboard. On Evinrude E-Tec's with a tiller steer, make sure the gear shift is in neutral position.
Finally, if you can, check for any disconnected wires from the key switch. If this is all good, then your boat will require more advanced troubleshooting to find the problem.