How do you fix 2005 mercury montego radio display?

If the display is not on when you turn the ignition on. First you check the fuses. radio memory is usually run with the courtesy light fuse. The main radio fuse is marked radio.

Second you pull the radio out and test the power leads to the radio. If you have no power then there may be a short in a wire.

If there is power on the power leads then the radio must be replaced.