My 360 wont turn on and the power convertor says its in standby mode. what do i do?

Are you using a plug and play charger? if you are remove the cable and have another go, this happens with mine sometimes.
Or have a look into the usb ports to the right of the console under the big flap,(this is easier if you remove the faceplate) see if there is any damage or any bent pins, this will short your console so it won't switch on, just make sure no pins are touching.
Remember thumbs up if this helps.

Did you Try to change your HDMI settings. If you did and your tv Does not have that high of a setting then the system wont turn on for safety reasons. There is a reset hole on the power supply box. Reset it.