Hi,
Good choice on your plane!
First NEVER turn off your transmitter while the plane is powered on. You will loose connection and control (depending how the plane is set-up) and it can be very dangerous. Always power on the transmitter first and the plane last and when shutting down always power down the plane first and the transmitter last.
Onto the motor issue. On the transmitter make sure the throttle(left stick) is lowered all the way and it's trim control is lowered all the way. Power on the transmitter and then plug the battery into the plane. When the battery is connected, you will hear one low long tone to indicate startup, then the respective number of medium-length mid tones to indicate the cell count or a musical tone, followed by three rising tones to indicate
the controller is armed. Once you hear the last 3 tones the motor is armed and the prop should turn as you raise the throttle.

If you don't hear the tones check the throttle and trim controls on the transmitter and make sure they are set to low, check the connections between the motor and the ESC(speed control), and check the receiver connections. If in doubt you can refer to the manual for radio set-up and power-on procedures.http://www.horizonhobby.com/pdf/EFL2...ice-Manual.pdf

As far as not being able to trim the plane , what exactly is the problem? The trim levers shouldn't be moved much in order to get the plane flying straight and level, if so something else is out of adjustment. If it's windy out the plane will bounce around , rise and fall, even if it's trimmed properly and make it seem as thought it's not .

Good luck