You can zoom to any geometry, so if you have the geometry or envelope of the state, you can simply do:
myMap.ZoomTo(geometry);
This will fit the state in the view.
Do you want the polygon of the state, or the point of where you right-clicked?
mapPoint = myMap.ScreenToMap(point);
The geometry doesn't need to be a polygon. It's working with a point as well.
Here is a sample : http://help.arcgis.com/en/webapi/silverlight/samples/start.htm#SpatialQuery
It looks like you missed to convert the screen coordinates to map coordinates.
Add something like:mapPoint = myMap.ScreenToMap(point);