What would cause the trunk button on a buick rendevous not to work

Most likely there is a fuse blown--OR the button switch solenoid is burnt out. check fuse panel first. If no fuse blown--find the 2 wires going into the trunk button solenoid. Temporarily remove a bit of insulation from both wires or if there are more than 2 wires--bare them all. Then take a small bare wire & QUICKLY touch from each one to the other to see if there's a spark--being ready to quickly remove it IF there's a spark. If there is a sparking--then the solenoid is likely gone. Recheck fuses to make sure you didn't blow the fuse by sparking the wires. If so, replace fuse & solenoid.