There should also be a switch (or switches) at the helm.
The way the trim system works is that there is 'trim' and there is 'tilt'. Theses are typically done by two separate switches. The trim switch will only raise the outdrive to the "Trim Limit", which is the highest point in which you can safely run the propeller. The 'Tilt' switch by-passes the 'limit' function and will raise the outdrive as much as you want until it reaches its highest point.
Boats are stupid and they don't know if they are in the water or not. It sounds like the switch at the transom (rear of the boat) is only a trim switch (???) unless it has both a trim and tilt button.
