It is important that your air conditioner be plugged into an outlet that is supplying the correct voltage. Check the specifications sheet for your particular model to determine the power requirements.
If your air conditioner requires a 208/230 volt power supply, the outlet must be rated to provide proper power to the unit. If you only changed the outlet to match the power cord plug, but did not have the outlet rewired, then the unit will not be receiving the correct power.
If your air conditioner uses a 115 volt power supply, the outlet has the correct voltage, but the breaker is tripping and causing the loss of power. A simple test can be performed to see if other devices are powered on the same circuit breaker as your outlet.
Turn off all other electrical devices in the room except for the air conditioner. If the air conditioner runs fine with other devices turned off, then likely the unit is not on a dedicated circuit breaker.
If the air conditioner is not on a dedicated circuit breaker, the unit may power on but not run. The reason for this is that the unit does not require as much power to display the settings, or even run the fan, as it does to turn on and run the compressor. The air conditioner must be on a dedicated circuit breaker not shared with other outlets.